Class 12

Sources of Corporate Finance 12th Secretarial Practice Chapter 2 Solutions Maharashtra Board

Balbharti Maharashtra State Board Class 12 Secretarial Practice Solutions Chapter 2 Sources of Corporate Finance Textbook Exercise Questions and Answers.

Class 12 Secretarial Practice Chapter 2 Exercise Solutions

1A. Select the correct answer from the options given below and rewrite the statements.

Question 1.
___________ is the smallest unit in the total share capital of the company.
(a) Debenture
(b) Bonds
(c) Share
Answer:
(c) Share

Question 2.
The benefit of Depository Receipt is ability to raise capital in ___________ market.
(a) national
(b) local
(c) international
Answer:
(c) international

Question 3.
___________ are residual claimants against the income or assets of the company.
(a) Bondholders
(b) Equity shareholders
(c) Debenture holders
Answer:
(b) Equity shareholders

Question 4.
___________ participate in the management of their company.
(a) Preference shareholders
(b) Depositors
(c) Equity shareholders.
Answer:
(c) Equity shareholders

Question 5.
___________ shares are issued free of cost to existing equity shareholders.
(a) Bonus
(b) Right
(c) Equity
Answer:
(a) Bonus

Question 6.
The holder of preference share has the right to receive ___________ rate of dividend.
(a) fixed
(b) fluctuating
(c) lower
Answer:
(a) Fixed

Question 7.
Accumulated dividend is paid to ___________ preference shares.
(a) redeemable
(b) cumulative
(c) convertible
Answer:
(b) Cumulative

Question 8.
The holder of ___________ preference shares has the right to convert their shares into equity shares.
(a) cumulative
(b) convertible
(c) redeemable
Answer:
(b) Convertible

Question 9.
Debenture holders are ___________ of the company.
(a) creditors
(b) owners
(c) suppliers
Answer:
(a) creditors

Question 10.
___________ is paid on borrowed capital.
(a) Interest
(b) Discount
(c) Dividend
Answer:
(a) Interest

Question 11.
Debenture holders get fixed rate of ___________ return on their investment.
(a) interest
(b) dividend
(c) discount
Answer:
(a) interest

Question 12.
Convertible debentures are converted into ___________ after a specific period.
(a) equity shares
(b) deposits
(c) bonds
Answer:
(a) equity shares

Question 13.
Retained earnings are ___________ source of financing.
(a) internal
(b) external
(c) additional
Answer:
(a) internal

Question 14.
The holder of bond is ___________ of the company.
(a) secretary
(b) owner
(c) creditor
Answer:
(c) creditor

Question 15.
Company can accept deposits from public, minimum for ___________ months.
(a) six
(b) nine
(c) twelve
Answer:
(a) six

Question 16.
Company can accept deposits from public maximum for ___________ months.
(a) 12
(b) 24
(c) 36
Answer:
(c) 36

Question 17.
A depository receipt traded in ___________ is called American Depository Receipt.
(a) London
(b) Japan
(c) USA
Answer:
(c) the USA

1B. Match the pairs.

Question 1.

Answer:

Group ‘A’	Group ‘B’
(a) Equity share capital	(1) Venture capital
(b) Debenture Trustees	(2) Trust Deed
(c) Preference shareholders	(3) Cautious investor
(d) Debenture Certificate	(4) Instrument of Debt
(e) Bonus shares	(5) Capitalisation of profit

1C. Write a word or a term or a phrase that can substitute each of the following statements.

Question 1.
The real masters of the company.
Answer:
Equity shareholders

Question 2.
A document of ownership of shares.
Answer:
Share certificate

Question 3.
The holders of these shares are entitled to participate in surplus profits.
Answer:
Participating preference shares

Question 4.
A party through whom the company deals with debenture holders.
Answer:
Debenture trustees

Question 5.
Name the shareholder who participates in the management.
Answer:
Equity shareholders

Question 6.
The value of a share is written on the share certificate.
Answer:
Face value

Question 7.
The value of a share is determined by demand and supply forces in the share market.
Answer:
Market value

Question 8.
The policy of using undistributed profit for the business.
Answer:
Retained earnings/ploughing back of profit

Question 9.
It is an acknowledgment of a loan issued by the company to the depositor.
Answer:
Deposit receipt

Question 10.
A dollar-denominated instrument trader in the USA.
Answer:
American Depository Receipt

Question 11.
The Depository Receipt is traded in a country other than the USA.
Answer:
Global depository receipt

Question 12.
Money raised by the company from the public for a minimum of 6 months to a maximum of 39 months.
Answer:
Public Deposits

Question 13.
Credit extended by the suppliers with an intention to increase their sales.
Answer:
Trade Credit

Question 14.
The credit facility is provided to a company having a current account with the bank.
Answer:
Overdraft

1D. State Whether the following statements are True or False.

Question 1.
Equity share capital is known as venture capital.
Answer:
True

Question 2.
Equity shareholders enjoy a fixed rate of dividends.
Answer:
False

Question 3.
Debenture holders have the right to vote at a general meeting of the company.
Answer:
False

Question 4.
Equity shareholders are described as ‘shock absorbers’ when a company has a financial crisis.
Answer:
True

Question 5.
Bondholders are owners of the company.
Answer:
True

Question 6.
Cash credit is given against hypothecation of goods and security.
Answer:
True

Question 7.
Trade credit is a major source of long-term finance.
Answer:
False

Question 8.
Depository bank stores the shares on behalf of the GDR holder.
Answer:
True

Question 9.
Financial institutions underwrite the issue of securities.
Answer:
True

1E. Find the odd one.

Question 1.
Debenture, Public Deposit, Retained Earnings
Answer:
Retained earnings

Question 2.
Face value, Market value, Redemption value
Answer:
Redemption value

Question 3.
Share certificate, Debenture certificate, ADR
Answer:
ADR

Question 4.
Trade credit, Overdraft, Cash credit
Answer:
Trade credit

1F. Complete the sentences.

Question 1.
The finance needed by business organisation is termed as ___________
Answer:
Capital

Question 2.
The convertible preference shareholders have a right to convert their shares into ___________
Answer:
Equity shares

Question 3.
Equity shareholders elect their representative Called ___________
Answer:
Directors

Question 4.
Bonus shares are issued as gift to ___________
Answer:
Equity share holders

Question 5.
The bondholders are ___________of the company.
Answer:
Creditors

Question 6.
Depository receipt traded in a country other than USA is called ___________
Answer:
Global Depository Receipt

Question 7.
First Industrial policy was declared in the year ___________
Answer:
1948

Question 8.
When goods are delivered by the supplier to the customer on the basis of deferred payment is called as ___________
Answer:
Trade credit

1G. Select the correct option from the bracket.

Question 1.

(Fluctuating rate of dividend, Preference shares, Interest at fixed rate, Retained earnings, short term loan)
Answer:

Group ‘A’	Group ‘B’
(a) Equity shares	(1) Fluctuating rate of dividend
(b) Preference shares	(2) Dividend at a fixed rate
(c) Debentures	(3) Interest at a fixed rate
(d) Retained earnings	(4) Accumulated corporate profit
(e) Public Deposit	(5) short term loan

1H. Answer in one sentence.

Question 1.
What is a share?
Answer:
A share is the smallest unit of the share capital of a company.

Question 2.
What are equity shares?
Answer:
Equity shares are shares that do not preference shares and do not carry priority in receiving dividends nor repayment of capital.

Question 3.
What are preference shares?
Answer:
Preference shares are shares that have preferential rights with regard to receiving dividends and repayment of capital.

Question 4.
What are retained earnings?
Answer:
A part of the net profit which is not distributed to shareholders as dividend but retained by the company as reserve fund is retained earnings.

Question 5.
What is a debenture?
Answer:
It is a document/instrument issued in the form of a debenture certificate under the common seal of the company acknowledging/evidencing the debt.

Question 6.
What is a bond?
Answer:
A bond is a debt security and a formal contract to repay borrowed money with interest.

Question 7.
In which country can ADR be issued?
Answer:
ADR (American Depository Receipt) is a depository Receipt that is issued in the USA.

Question 8.
In which country can GDR be issued?
Answer:
GDR (Global depository receipt) can be issued in countries other than the USA.

Question 9.
What are convertible debentures?
Answer:
Convertible debentures are debentures that are converted into equity shares after a specific period as specified at the time of issue.

Question 10.
What are cumulative preference shares?
Answer:
Cumulative preference shares are shares where dividend, if not paid in a year accumulates till it is paid.

1I. Correct the underlined words and rewrite the following sentences.

Question 1.
Owned capital is temporary capital.
Answer:
Owned capital is permanent capital.

Question 2.
Equity shares get dividends at a fixed rate.
Answer:
Equity shares get dividends at fluctuating rates.

Question 3.
Preference shares get dividends at fluctuating rates.
Answer:
Preference shares get dividends at a fixed rate.

Question 4.
Retained earnings are an external source of finance.
Answer:
Retained earnings are an internal source of finance.

Question 5.
The debenture holder is the owner of the company.
Answer:
The debenture holder is a creditor of the company.

Question 6.
Bond is a source of short-term finance.
Answer:
Bond is a source of long-term finance.

Question 7.
Depository receipt traded in the USA is called Global Depository Receipt.
Answer:
Depository receipt traded in the USA is called American Depository Receipt.

2. Explain the following terms/Concepts.

Question 1.
Borrowed capital
Answer:

• It consists of capital that is raised through borrowings.
• It can be raised by issuing debentures, deposits, loans from banks or financial institutions.

Question 2.
Owned capital
Answer:

• Owned capital is the capital raised by the company with the help of owners (shareholders).
• It can be raised by issuing equity and preference shares.

Question 3.
Ploughing back of profit
Answer:

• Ploughing back of profit or retained earnings is a management policy under which all profits are not distributed amongst shareholders.
• It is an internal source of financing or self-financing as when the need arises, such reserves are ploughed back, brought into the business to meet the financial needs.

Question 4.
Overdraft
Answer:

• It is a credit agreement made with a bank that allows an account holder to withdraw more money than what a company has in its account up to a specific/prescribed limit.
• This facility is available to current account holders.

Question 5.
Trade Credit
Answer:

• Trade credit is credit extended by one trader to another when goods and services are bought/sold on credit.
• It facilitates the purchase of supplies without making an immediate payment.
• It is used by business organisations as a source of short-term financing and granted to those having reasonable standing and goodwill.

3. Study the following case/situation and express your opinion.

1. The Balance sheet of a Donald Company for the year 2018-19 reveals equity share capital of Rs. 25,00,000 and retained earnings of Rs. 50,00,000.

Question (a).
Is the company financially sound?
Answer:
The company is financially sound as it has double the amount as reserves or retained earnings or kept aside profits.

Question (b).
Can the retained earnings be converted into capital?
Answer:
Yes, the retained earnings can be converted into capital by means of capitalisation of reserves.

Question (c).
What type of source retained earning is?
Answer:
Retained earning is self-financing or an internal source of finance.

2. Mr. Satish is a speculator. He desires to take advantage of the growing market for the company’s products and earn handsomely.

Question (a).
According to you, which type of share Mr. Satish will choose to invest in.
Answer:
As Mr. Satish is a speculator, he will choose equity shares to invest in because if there are good earnings/profits, so will be the rate of dividend.

Question (b).
What does he receive as a return on investment?
Answer:
He receives a fluctuating rate of dividends.

Question (C).
State anyone, right he will enjoy as a shareholder.
Answer:
The right to attend the meeting and vote on resolutions can be the right Mr. Satish can exercise as a member.

3. Mr. Rohit, an individual investor, invests his own funds in the securities. He depends on investment income and does not want to take any risk. He is interested in the definite rate of income and safety of the principal.

Question (a).
Name the type of security that Mr. Rohit will opt for.
Answer:
As Mr. Rohit does not want to take risks, he will opt for preference shares which will assure him of steady income and safety of his investment.

Question (b).
What does he receive as a return on his investment?
Answer:
Mr. Rohit will receive dividends in return.

Question (c).
The return on investment which he receives is fixed or fluctuating.
Answer:
The return on his investment will be fixed and not fluctuating.

4. Distinguish between the following.

Question 1.
Equity Shares and Preference Shares
Answer:

Points	Equity Shares	Preference Shares
1. Meaning	Shares that are not preference shares are called equity shares i.e. these shares do not have the preferential rights for payment of dividends and repayment of capital.	Preferences shares are shares that carry preferential rights as to payment of: Dividend and Repayment of capital.
2. Rate of Dividend	Equity shares are given dividends at a fluctuating rate depending upon the profits of the company.	Preference shareholders get dividends at a fixed rate.
3. Voting Right	Equity shareholders enjoy normal voting rights. They participate in the management of their company.	Preference shareholders do not enjoy normal voting right. They can vote only on matters affecting their interest.
4. Return of Capital	Equity capital can not be returned during the lifetime of the company, (except in case of buyback).	A company can issue redeemable preference shares, which can be repaid during the lifetime of the company.
5. Nature of capital	Equity capital is known as ‘Risk Capital’.	Preference capital is ‘Safe Capital’ with a stable return.
6. Nature of investor	The investors who are ready to take risks to invest in equity shares.	Investors who are cautious about the safety of their investment invest in preference shares.
7. Face Value	The face value of equity shares is generally ₹ 1/- or ₹ 10/- it is relatively low.	The face value of preference shares is relatively higher i.e. ₹ 100/- and so on.
8. Right and bonus issue	Equity shareholder is entitled to get bonus and right issue.	Preference shareholders are not eligible for bonuses and right issues.
9. Capital appreciation	The market value of equity shares increases with the prosperity of the company. It leads to an increase in the value of shares.	The market value of preference shares does not fluctuate, so there is no possibility/cheques of capital appreciation.
10. Risk	Equity shares are subject to higher risk.	Preference shares are subject to less risk.
11. Types	Equity shares are classified into: Equity shares with normal voting rights. Equity shares with differential voting rights.	Preference shares are classified as: Cumulative Preference Shares Non-Cumulative Preference Shares Convertible Preference Shares Non-Convertible Preference Shares Redeemable Preference Shares Irredeemable Preference Shares Participating Preference Shares Non-Participating Preference Shares

Question 2.
Shares and Debentures
Answer:

Points	Shares	Debentures
1. Meaning	Share is the smallest unit in the total share capital of the company. It is known as ownership securities.	A debenture is an instrument evidencing debt under the seal of the Company. They are also known as creditor ship securities.
2. Status	A holder of shares is the owner of the company. Hence, share capital is owned capital.	A holder of debenture is the creditor of the company. Hence, Debenture capital is loan capital or borrowed capital.
3. Nature	It is permanent capital. It is not repaid during the lifetime of the company.	It is temporary capital. Generally, it is repaid after a specific period.
4. Voting/Right	Shareholders being owners enjoy normal voting rights in general meetings and can participate in the management of the company.	Debenture holders being creditors, do not have any voting right and can not participate in the management of the company.
5. Return on Investment	Return on shares is called a dividend. Equity shareholders receive dividends at a fluctuating rate whereas preference shareholders receive dividends at a fixed rate.	Return on debenture is called interest. It is fixed at the time of issue. Interest is paid even when a company has no profit.
6. Security	Share capital is unsecured capital. No security is offered to the shareholder.	Debenture capital being loan capital is secured by creating a charge on Company’s property.
7. Time of Issue	Shares are issued in the initial stages of the company formation.	Debentures are issued at a later stage when the company has properties to offer as security.
8. Suitability	Shares are suitable for long-term finance.	Debentures are suitable for medium-term finance.
9. Types	Shares are classified into: Equity shares Preference	A debenture is classified as: Registered Debentures Bearer Debentures Secured Debentures Unsecured Debentures Redeemable Debentures Irredeemable Debentures Convertible Debentures Non-Convertible Debentures
10. Position on liquidation	On liquidation of a company, shareholders rank last in the list of claimants.	Debenture holders being creditors, rank prior to shareholders for repayment on liquidation of the company.

Question 3.
Owned Capital and Borrowed Capital
Answer:

Points	Owned Capital	Borrowed Capital
1. Meaning	It is that capital that is contributed by shareholders.	It is that capital that is borrowed from creditors. It is also known as debt capital.
2. Sources	This capital is collected by the issue of equity shares and preference shares, ploughing back of profits (ownership securities).	It is collected by way of the issue of debentures, fixed deposits, loans from banks/financial institutions, etc. (loan, borrowings).
3. Return on Investment	The shareholders get dividends as income on their investment. The rate of dividend is fluctuating, in the case of equity shares but is fixed in the case of preference shares.	The debt capital holders get interested as income on their investment. Interest is paid at a fixed rate.
4. Status	The shareholders are owners of the company.	The debt holders are creditors of the company.
5. Voting right	The equity shareholders enjoy normal voting right at the general meetings.	The creditors do not enjoy voting rights at the general meeting.
6. Repayment of Capital Redemption	The shareholders do not enjoy priority over creditors. They are eligible for repayment of Capital only after making payment to creditors at the time of windings up of the company.	The creditors get priority over the shareholders in case of return of principal amount at the time of winding up of the company.
7. Charge on assets	The shareholders do not have any charge on the assets of the company.	The secured debenture holders have a change on the assets of the company.

5. Answer in brief:

Question 1.
What is a public deposit?
Answer:

• Public deposit is an important source of financing short-term requirements of the company.
• Companies generally receive public deposits for a period ranging from 6 months to 36 months.
• Interest is paid by the companies on such deposits.
• The company issues a’ Deposit Receipt’ to the depositor.
• The receipt is an acknowledgment of debt/loan by the company.
• Deposits are either secured or unsecured loans offered by a company.
• It is considered a risky investment but investors can earn high returns on public deposits.

Advantages of deposits to the company

• It is an easier method of mobilizing funds during periods of credit squeeze.
• The rate of interest payable by the company on public deposits is lower than the interest from banks and financial institutions.
• It helps the company to borrow funds from a larger segment and thus, reduces dependence on financial institutions.

Question 2.
What are Global Depository Receipt and American Depository Receipt?
Answer:

• The shares that are issued by public limited companies are traded in various share markets.
• In India, shares are traded in the Bombay Stock Exchange (BSE) National Stock Exchange (NSE), etc.
• Similarly, Shares are traded in foreign stock exchanges like NYSE (New York Stock Exchange) or NASDAQ (National Association of Securities Dealers Automated Quotation).
• Companies that cannot list directly on foreign stock exchange get listed indirectly using GDR & ADR.
• GDR and ADR are Dollar/Euro denominated instruments traded on stock exchanges of foreign countries and are depository receipts containing a fixed number of shares.
• The Depository Receipts which are traded in the USA are called ADRs and Depository Receipts which are traded in all foreign countries other than the USA are called GDR.
• Indian Companies raise equity capital in the international market through GDR and ADR.
• Companies issue shares to an intermediary called ‘depository’.
• Bank of New York, Citigroup, etc act as Foreign Depository Bank.
• The Depository Banks issue GDRs or ADRs to investors against Indian Company’s shares.
• These ‘Depository Receipts’ are then, sold to foreign investors who wish to invest their savings in Indian Cost.
• The Depository Receipts are listed on the stock exchanges like regular shares.
• It is a depository bank that stores the shares on behalf of the receipt holder.
• NRI and foreign investors buy Depository Receipt Using their regular equity trading account.
• The company pays dividends in the home currency to the depository and the depository converts them into the currency of investor and pays dividends.
• Indian Companies like HDFC, ICICI, Infosys Technologies, MTNL, WIPRO have ADR and GDR.
  • Tata Motors and VSNL have ADRs.
  • Bajaj Auto Limited ITC, L&T, Hindalco, Ranbaxy Laboratories, and SBI have GDRs.
  • ADR allows the sale of securities only in the American market whereas GDR allows the sale of securities globally.

Question 3.
What is Trade Credit?
Answer:

• Every business requires trade credit and is common to all business types.
• Credit sales or granting of credit is inevitable in the present competitive business world.
• It is short-term financing to businesses.
• The small retailers, to a large extent, rely on obtaining trade credit from their suppliers.
• The cheapest method of financing; it is an easy kind of credit that can be obtained without signing any debt instrument.
• This is not a cash loan. It results from a sale of goods services which have to be paid sometime after the sale takes place.
• It is given by one trader to another trader to delay payment for goods and services involved in the transaction.
• Suppliers sell goods and willingly allow 30 days or more credit period for the bill to be paid.
• They offer discounts if bills are cleared within a short period such as 10 or 15 days.
• Such credit is given/granted to those having reasonable standing and goodwill.

Advantages of Trade Credit:

• Trade Credit is the cheapest and easiest method for raising short-term finance.
• It can be obtained without making any formal and written agreement or signing the same.
• It is readily available whenever goods and services are purchased on credit in bulk.
• It is free of cost source of financing.
• The terms of trade are lenient and not rigid.

Question 4.
What are the schemes for disbursement of credit by banks?
Answer:
Meaning: Banks play an important role in terms of providing finance to the companies.
They provide short-term finance for working capital, in the form of bank and trade credits.

The innovative schemes by banks for disbursement of credit are as follows:
(i) Overdraft:

• A company having a current account with the bank is allowed an overdraft facility.
• The borrower can withdraw funds/overdraw on his current account up to the credit limit sanctioned by the bank.
• Any number of drawings up to the sanctioned limit is allowed for a stipulated term period.
• Interest is determined/calculated on the basis of the actual amount overdrawn.
• Repayments can be made during the time period.

(ii) Cash Credit:

• The borrower can withdraw the amount from his cash credit up to a stipulated/granted limit based on security margin.
• Cash credit is given against pledge or hypothecation of goods or by providing alternate securities.
• Interest is charged on the outstanding amount borrowed and not on the credit limit sanctioned.

(iii) Cash Loans:

• In this, the total amount of the loan is credited by the bank to the borrower’s account.
• Interest is payable on the actual outstanding balance.

(iv) Discounting bills of exchange:

• In the bill of exchange, the drawer of the bill (seller) receives money from the drawee (buyer) on the date or after the due date (the term mentioned in the bill).
• But due to discounting facility the drawer can receive money before the due date by discounting the bill with the bank (by giving the bill as security to the bank).
• The bank gives money to the drawer less than the face value of the bill (amount mentioned in the bill) after deducting a certain amount known as discounting charges.
• The bills are usually traded bills i.e. outcome of trade transactions.
• The bills are accepted by the banks and cash is advanced against them.

Question 5.
State the features of bonds.
Answer:
Definition:
According to Webster Dictionary, “a bond is an interest bearing certificate issued by a Government or business firm promising to pay the holder a specific sum at a specified date”.
A bond is thus-

• A formal contract to repay borrowed money with interest.
• Interest is payable at a fixed internal or on the maturity of the bond.
• A bond is a loan.
• The holder is a lender to the company.
• He gets a fixed rate of interest.

Features:
(i) Nature of finance:

• It is debt or loan finance.
• It provides long-term finance of 5 years, 10 years, 25 years, 50 years.

(ii) Status of investor:

• The bondholders are creditors.
• They are non-owners and hence, not entitled to participate in the general meetings.
• The bondholder has no right to vote.

(iii) Return on bonds:

• The bondholders get a fixed rate of interest.
• It is payable on maturity or at a regular interval.
• Interest is paid to the bondholder at a fixed rate.

(iv) Repayment:

• A bond is a formal contract to repay borrowed money.
• Bonds have a specific maturity date, on which the principal amount is repaid.

6. Justify the following statements:

Question 1.
Equity shareholders are real owners and controllers of the company.
Answer:

• They do not have special preferential rights as to dividends or returns of capital in the event of the winding-up of the company.
• They are joint owners and thus, have ownership rights.
• They have the right to participate in the management of the company and to vote on every resolution in the meetings thus, having exclusive voting rights.
• They use the right to vote to appoint directors, amend Memorandum of Association, Articles of Association, can remove directors appoint bankers, etc.
• Their shares bear ultimate risks associated with ownership.
• Thus, it is rightly said, that the equity shareholders are real owners and controllers of the company.

Question 2.
Preference Shares do not carry normal voting rights.
Answer:

• Preference shares enjoy priority or preference over equity shareholders as regards payment of dividends and repayment of capital.
• They carry a fixed rate of dividend.
• They do not take much risk as they are cautious investors.
• They attend class meetings if they have any problem affecting their interests or dividend is not paid to them for two or more consecutive years.
• As they do not take risks, they do not attend general meetings or take part in the management nor vote at the meetings.
• Thus, it is rightly said, that the preference shares do not carry voting rights.

Question 3.
The debenture is secured by a charge on assets of the company.
Answer:

• A debenture is a document that grants lenders a charge over a company’s assets giving them a means of collecting debt if a default occurs.
• The charges may be floating or fixed.
• A specific property is pledged as security.
• In case the debenture is not redeemed or exercised, the lenders can recover the cost by selling the fixed assets.
• Thus, it is rightly said, that the debenture is secured by a charge on assets of the company.

Question 4.
Retained earnings are the simple and cheapest method of raising finance.
Answer:

• Retained earnings is an internal source of financing used by established companies.
• Retained earnings is a kept aside profit by the company instead of distributing all the dividends to the shareholders.
• The accumulated profits are re-invested by the companies by issuing bonus shares.
• It does not create a charge on assets, nor dilute the shareholdings.
• Thus, it is rightly said, that the retained earnings also known as ploughing back of profit/capitalization of reserves/self-financing are the simple and cheapest methods of raising finance.

Question 5.
Public deposit is a good source of short-term financing.
Answer:

• Deposits can be accepted by the general public by public limited companies and not private limited companies.
• Deposits are accepted from the general public for a short term i.e. minimum 6 months and a maximum of 36 months or a 3-year term.
• The amount so raised is used for short-term financial requirements.
• The time of deposit is predetermined in advance and paid after the expiry of such period as per terms and conditions agreed.
• The depositors form the general public not necessarily equity shareholders.
• The administrative cost of deposits of the company is lower than that involved in the issue of shares and debentures.
• The rate of interest payable is lower than other loans. Thus, it is rightly said, that the public deposit is a good source for meeting short-term requirements.

Question 6.
The bondholder is a creditor of the company.
Answer:

• A bond is a debt security which the company borrows for long-term finance and issues certificates under its seal as acknowledgment.
• The owners get interested as a return on their investment which is decided and fixed at the time of issue.
• The interest payable to bondholders is a fixed charge and a direct expenditure.
• It has to be paid whether the company makes a profit or not.
• As the bondholders are creditors they do not have the right to attend meetings or participate in management.
• Thus, it is rightly said, that the bondholder is a creditor of the company.

Question 7.
Trade credit is not a cash loan.
Answer:

• Trade credit is a business-to-business agreement wherein there is an arrangement to purchase goods and services on credit and pays at a later date and not immediately.
• The credit period extends up to a month.
• Discount is given if the same is paid earlier.
• It is an interest-free loan given by one businessman to another.
• It does not involve loan formalities but only a trade transaction. Hence, not a cash loan.
• Thus, it is rightly said, that the trade credit is not a cash loan.

Question 8.
Different investors have different preferences.
Answer:

• Investors make different decisions and have different risk preferences when getting gains and losses.
• Educated ones may opt for capital markets as compared to others who may invest in gold or silver.
• Cautious investors are ready to have steady income rather than fluctuations.
• Risk-takers are ready to face the ups and downs of their invested money and on their returns.
• Active investors try to beat the market while passive track the market index.
• Thus, it is rightly said, that the different investors have different choices and preferences.

Question 9.
Equity Capital is risk capital.
Answer:

• Equity shareholders have a claim over residual proceeds of the company.
• In the event of winding up, they are the last to be paid off after setting the claims of creditors and external liabilities.
• They have fluctuating returns and risk of fluctuating market value.
• Equity capital is permanent capital and not refunded during the lifetime of the company.
• Not having any assurance as regards dividend, repayment of capital Equity Capital becomes risk capital.
• Thus, it is rightly said, that equity capital is risk capital.

7. Answer the following questions.

Question 1.
What are a share and state its features?
Answer:

• The term share is defined by section 2(84) of the Companies Act 2013 ‘Share means a share in the share capital of a company and includes stock.’ The capital of a company is divided into a large number of shares.
• It facilitates the public to subscribe to the company’s capital in smaller amounts.
• The share is thus, an indivisible unit of share capital.
• It is a unit by which the share capital is divided.
• The total capital is divided into small parts and each such part is called a share.
• The value of each part/unit is known as face value.
• A person can purchase any number of shares as and when he or she desires.
• A person who purchases shares of the company is known as a shareholder of the company.
• Generally, companies issue equity shares and preference shares in the market.

Features of shares:
(i) Meaning:

• Share is the smallest unit in the total share capital of a company.
• The total share capital of a company is divided into small parts and each part is called a share.

(ii) Ownership:

• A share shows the ownership of the shareholder.
• The owner of the share is called a shareholder.

(iii) Distinctive number:

• Unless dematerialized, each share has a distinct number, which is noted in the share certificate.
• A share has a distinct number for identification.

(iv) Evidence of title:

• The company issues a share certificate under its common seal.
• It is a document of title of ownership of the share.
• A share is not a visible thing.
• It is shown by share certificate or in the form of ‘Demat share’

(v) Value of a share:

• Each share has a value expressed in terms of money.
• Face value: This value is written on the share certificate and mentioned in the Memorandum of Association.
• Issue Value: It is the price at which a company sells its shares. At par – equal to face value; At premium – more than the face value; At discount – Less than the face value.

(vi) Rights:

• A share confers/gives certain rights to the shareholders.
• Rights such as the right to receive dividends, right to inspect statutory books, right to attend shareholders’ meetings, right to vote in meetings, etc. (group rights), and right to receive notice, circulars, dividends, bonus shares, rights issue, etc. (individual rights).

(vii) Income:

• A shareholder is entitled to get a share in the net profit of the company.
• It is called a dividend.

(viii) Transferability:

• The shares of the public Ltd. company are freely transferable as per the rules laid down in the Articles of Association.
• Shares of a private company cannot be transferred.

(ix) Property of shareholder:

• A share is a movable property of a member.
• It can be transferred (gifted, sold) or transmitted (passed on to the legal heir after/due to death, insolvency or insanity of a member).

(x) Kinds of shares:

• A company issues two types of shares depending upon the right to control, income and risk.
• Equity shares – which do not carry preferential right to receive dividend or repayment of capital when the company winds up its activities.
• Preference shares – which carry preferential rights as regards dividend and repayment of capital in the event of winding up of the company.

Question 2.
What is an equity share? Explain its features.
Answer:

• Equity shares are the fundamental and basic source of financing activities of the business.
• Equity shares are also known as ordinary shares.
• Indian Companies Act 1956 defines equity shares as those shares which do not preference shares.
• The equity shares do not enjoy a preference in getting dividends.

Features of equity shares:
(i) Permanent Capital:

• Equity shares are irredeemable shares. It is permanent capital.
• The amount received from equity shares is not refunded by the company during its lifetime.
• Equity shares become redeemable/refundable only in the event of the winding-up of the company or the company decides to buy back shares.
• Equity shareholders provide long-term and permanent capital to the company.

(ii) Fluctuating dividend:

• Equity shares do not have a fixed rate of dividend.
• The rate of dividend depends upon the amount of profit earned by the company.
• If a company earns more profit, the dividend is paid at a higher rate.
• If there is insufficient profit, the Board of Directors may postpone the payment of dividends.
• The shareholders cannot compel them to declare and pay the dividend.
• The dividend is thus, always uncertain and fluctuating.
• The income of equity shares is uncertain and irregular.

(iii) Rights:

• Equity shareholders enjoy certain rights.
• Right to share in profit when distributed as dividend.
• Right to vote by which they elect Directors, amend Memorandum, Articles, etc.
• Right to inspect books of account of their company.
• Right to transfer shares.
• Participation in management.
• Enjoy Right Issue and Bonus Issue.

(iv) No preferential right:

• Equity shareholders do not enjoy preferential rights in respect to the payment of dividends.
• They are paid dividends only after the dividend is paid to preference shareholders.
• At the time of winding up, they are the last claimants. They are paid last after all the other claims are settled.

(v) Controlling power:

• The control of a company vests in the hands of equity shareholders.
• They are often described as real masters of the company as they enjoy exclusive voting rights.
• Equity shareholders may exercise their voting right by proxies, without attending the meeting in person.
• The Act provides the right to cast vote in proportion to the number of shareholdings.
• They participate in the management of the company.
• They elect their representatives called the Board of Directors for management of the company.

(vi) Risk:

• Equity shareholders bear maximum risk in the company.
• They are described as ‘shock absorbers when the company is in a financial crisis.
• The rate of dividend falls if the income of the company falls.
• The market value of shares goes down resulting in capital loss.

(vii) Residual claimants:

• A residual claim means the last claim on the earnings of the company.
• Equity shareholders are owners and they are residual claimants to all earnings after expenses, taxes, dividends, interests are paid.
• Even though equity shareholders are the last claimants, they have the advantage of receiving the entire earnings that are leftover.

(viii) No charge on assets:

• The equity share does not create any charge over the assets of the company.
• There is no security/guarantee of capital invested being returned.

(ix) Bonus issue:

• Bonus shares are issued as gifts to equity shareholders.
• They are issued ‘free of cost’.
• These shares are issued out of accumulated profits.
• These shares are issued to existing equity shareholders in a certain ratio or proportion of their existing shareholdings.
• Capital investment of equity shareholders grows on its own.
• This facility is available only to equity shareholders.

(x) Rights issue:

• Equity shareholders get the benefit of rights issues.
• When a company raises further capital by issue of shares, the existing shareholders are given priority to get newly offered shares, known as a rights issue.

(xi) Face value:

• The face value of equity share is very less.
• It can be ₹ 10 per share or even ₹ 1/- per share

(xii) Market value:

• Market value fluctuates, according to the demand and supply of shares.
• The demand and supply of equity shares depend on profits earned and dividends declared.
• When a company earns huge profits, the market value of shares increases.
• When it incurs a loss, the market value of shares decreases.
• There are frequent fluctuations in the market value of shares in comparison to other securities.
• Equity shares are more appealing to speculators.

(xiii) Capital Appreciation:

• Share capital appreciation takes place when the market value of share increases in the share market.
• The profitability and prosperity of a company enhance the reputation of the company in the share market and thus, facilitates appreciation of the market value of equity shares.

Question 3.
Define preference shares/What are preference shares? What are the different types of preference shares?
Answer:

• These shares have certain privileges and preferential rights such as to payment of dividends, return of capital, etc.
• Preference Share has which fixed rate of dividend is prescribed at the time of issue.
• The preference shareholders are co-owners but not controllers.
• They are cautious investors as they are interested in the safety of the investment.

(i) Cumulative Preference Shares:

• Cumulative preference shares are those shares on which dividend accumulates until it is fully paid.
• That is if the dividend is not paid in one or more years due to inadequate profit, then such unpaid dividend gets accumulated and is carried forward till next year.
• The accumulated dividend is paid when the company performs well.
• The arrears of dividends are paid before making payment to equity shareholders.
• The preference shares are always cumulative unless otherwise stated in Articles of Association.

(ii) Non-Cumulative Preference Shares:

• The dividend on these shares does not accumulate.
• That is the dividend on shares can be paid only out of profits of that particular year.
• The right to claim dividends will lapse if the company does not make a profit in that particular year.
• If the dividend is not paid in a year, it is lost.

(iii) Participating Preference Shares:

• The holders of these shares are entitled to participate in surplus profit besides preferential dividends. They participate in the high-profit condition of the company.
• Surplus profit here means excess profit that remains after making payment of dividends to equity shareholders.
• Such surplus profit up to a certain limit is distributed to preference shareholders.

(iv) Non-Participating Preference Shares:

• The preference shares are deemed to be non-participating if there is no clear provision in Articles of Association regarding participation in surplus profit.
• Such shareholders are entitled to receive a fixed rate of a dividend prescribed in the issue.

(v) Convertible Preference Shares:

• These shares have a right to convert their preference shares into equity shares.
• The conversion takes place within a certain agreed fixed period.

(vi) Non-Convertible Preference Shares:

• These shares are not converted into equity shares.
• They will remain as preference shares forever till paid back.

(vii) Redeemable Preference Shares:

• Shares that can be redeemed after a certain fixed period are called redeemable preference shares.
• A company limited by shares if authorized by Articles of Association issues redeemable preference shares.
• Such shares must be fully paid.
• The shares are redeemed out of divisible profit or out of the fresh issue of shares made for this purpose.

(viii) Irredeemable Preference Shares:

• Shares which are not redeemable are payable only on winding up of the company and are called irredeemable preference shares.
• As per section 55(1) of the Companies Act 2013, the company cannot issue irredeemable preference shares in India.
• Thus, are the types of preference shares.

Question 4.
What are preference shares? State its features.
Answer:

• The shares which carry preferential rights are termed preference shares.
• These shares have certain privileges and preferential rights such as payment of dividend, return of capital, etc.
• The preference shareholders are co-owners but not controllers.
• They are cautious investors as they are interested in the safety of the investment.
• They prefer a steady rate of returns on investment.

Features of preference shares:
(i) Preference for dividend:

• They have the first charge on the distributable amount of annual profits.
• The dividend is payable to preference shareholders before anything else is paid to equity shares, but after the settlement of dues of debentures, bonds and loans.

(ii) Prior repayment of capital:

• Preference shareholders have a preference over equity shareholders in respect of return of capital when the company is liquidated.
• It saves preference shareholders from capital losses.

(iii) Fixed return:

• These shares carry dividends at a fixed rate.
• The rate of dividend is predetermined at the time of issue.
• It may be in the form of a fixed sum or may be calculated at a fixed rate.
• The preference shareholders are entitled to dividends which can be paid only out of profit.
• Though the rate of dividend is fixed, the director in the financial crisis of the company may decide that no dividend be paid if there are no profits, the preference shareholders would have no claims for the dividend.

(iv) Nature of capital:

• Preference share capital is safe capital as the rate of dividend and market value do not fluctuate.
• Preference shares do not provide permanent share capital.
• They are redeemed after a certain period of time.
• It is generally issued at a later stage when a company gets established business.
• They are used to satisfy the need for additional capital of the company.

(v) Market value:

• The market value of preference shares does not change as the rate of dividend payable to them is fixed.
• The capital appreciation is considered to be low as compared with equity shares.

(vi) Voting right:

• The preference shares do not have normal voting rights.
• They have voting rights in matters that affect their interests – change of rights in terms of repayment of capital, or dividend payable to them are in arrears for two or more years.

(vii) Risk:

• Cautious investors generally purchase preference shares.
• Safety of capital and fixed return on investment are advantages attached with preference shares.
• These shares are a boon for shareholders during the depression when the interest rate is continuously falling.

(viii) Face value:

• The face value of preference shares is relatively higher than equity shares.
• They are normally issued at a face value of ₹ 100/-

(ix) Right or Bonus issue:

• Preference shareholders are not entitled to bonus or rights issues.
• It can be issued to the equity shares only.

(x) Nature of investor:

• Preference shares attract a moderate type of investors.
• Investors who are conservative, cautious, interested in the safety of capital, expect a steady rate of returns on investment purchase preference shares.

Question 5.
What is Debenture/Define Debenture. Discuss the different types of Debentures.
Answer:

• Debentures are one of the main sources of raising debt capital for meeting long-term and medium-term financial needs.
• Debentures represent borrowed capital.
• A person who purchased debenture is called a debenture holder.
• The holders get a fixed rate of interest as a return on their investment.
• The Board of Directors has the power to issue debentures.

Definitions:
Topham defines: “A debenture is a document given by a company as evidence of debt to the holder, usually arising out of the loan and most commonly secured by the charge.”

They are as follows:
(i) Secured Debentures:

• The debentures can be secured.
• The property of a company is charged as security for the loan.
• The security may be for some particular asset (fixed charge) or it may be the asset in general (floating charge).
• The debentures are secured through ‘Trust Deed’.

(ii) Unsecured Debentures:

• These debentures do not have security.
• The issue of unsecured debentures is prohibited by the Companies Act, 2013.

(iii) Registered Debentures:

• They are the ones whose details are mentioned in the Register of debenture maintained by the company.
• The details include the name, address, particulars of
• The transfer of such debentures requires the execution of regular transfer deeds.
• Interest is paid through Dividend warrants.

(iv) Bearer Debentures:

• The details of the debentures are not recorded in the register of the debenture.
• Their names do not appear in the Register of Debenture Holders.
• Such debentures are transferred by mere delivery.
• Payment of interest is made by means of coupons attached to the debentures certificate.

(v) Redeemable Debentures:

• Debentures are mostly redeemable i.e. payable at the end of some fixed period, mentioned on the Debentures Certificate.
• Repayment may be made at a fixed date, at the end of a specific period, or six installments during the lifetime of the company.
• The provision of repayment is normally made in Trust Deed.

(vi) Irredeemable Debentures:

• These debentures are not repayable during the lifetime of the company.
• They are repayable only on liquidation of the company or when there is a breach of any condition or in contingencies.

(vii) Convertible Debentures:

• These debentures give the right to the holder to convert the debentures into equity shares after a specific period.
  the period of conversion is mentioned in the debenture certificate.
• The issue must be approved by a special resolution in the general meeting before they are issued to the public.
• A Convertible debentures holder is hence entitled to equity shares at a rate lower than the market value after which he can participate in the profits and meetings of the company.

(viii) Non-Convertible Debentures:

• These are not convertible into equity shares on maturity.
• They are normally redeemed on the maturity date.
• There is no appreciation in their value which acts as a disadvantage.

Question 6.
Define Debenture/What is a debenture? Explain the features of debenture?
Answer:

• A debenture is one of the main sources of raising debt capital for meeting long-term and medium-term financial needs.
• Debentures represent borrowed capital.
• A person who purchases debenture is called a debenture holder.
• The holders get a fixed rate of interest as a return on their investment.
• The Board of Directors has the power to issue debentures.

Definitions:
Topham defines: “A debenture is a document given by a company as evidence of debt to the holder, usually arising out of the loan and most commonly secured by the charge.”
A debenture is evidence of indebtedness.

Features of Debenture:
(i) Written Promise:

• A debenture is a written promise by a company that it owes a specified sum of money to the holder of the debenture.

(ii) Face Value:

• The face value of debenture normally carries a high denomination.
• It is ₹ 100 or multiples of ₹ 100.

(iii) Time of payment:

• A debenture is issued with the due date stated in the Debenture Certificate.
• It provides for repayment of the principal amount on the maturity date.

(iv) Priority of Payment:

• Debenture holders have a priority in repayment of their capital over other claimants of the company.
• The amounts of debentures are settled before shareholders.

(v) Assurance of repayment:

• Debenture constitutes a long-term debt.
• They carry an assurance of repayment on the due date.

(vi) Terms of issue and redemption of Debenture:

• Debenture can be issued at par, premium, and even at discount.
• Its redemption takes place only at par and premium.

(vii) Authority to issue:
Board of Directors has the authority/power to issue debenture as per Companies Act 2013 Section 179(3).

(viii) Interest:

• A fixed-rate of interest is agreed upon and is paid periodically.
• The rate of interest that a company pays/offers depends upon the market conditions and nature of the business.
• Payment of interest is a liability of the company. It has to be paid whether the company makes a profit or not.

(ix) Parties to Debenture:

• Company: This is an entity that borrows money.
• Trustees: The company has to appoint Debenture Trust if it is offering debenture to more than 500 people.
• Trust is a party through whom the company deals with debenture holders and enters into an agreement known as Trust Deed.
• Trust Deed contains obligations of the company rights of debenture holders, power of trustees, etc.
• Debenture holders: They are the parties who provide loans to the company and receive a ‘Debenture Certificate’ as evidence.

(x) Status of debenture holder:

• The debenture holder is a creditor of the company.
• Debenture being loan taken by the company interest is payable on it at a fixed interval and fixed-rate till redeemed/paid.
• They cannot participate in the management of the company.

(xi) No Voting Right:

• According to sec. 71 (2) of Companies Act 2013, no company shall issue debenture carrying voting rights.
• Debenture holders do not have the right to vote in the general meetings of the company.

(xii) Security:

• Debenture can be secured with some property of the company by fixed or floating charge.
• Debenture holders can sell of charged property of the company and recover their money if the company is not in a position to make payment of interest or repayment of capital.

(xiii) Issuers:

• Debenture can be issued by both, private as well as public limited companies.

(xiv) Listing:

• A debenture must be listed with at least one recognized stock exchange.

(xv) Transferability:

• Debentures can be easily transferred through instruments of transfer.

Maharashtra State Board 12th Std Secretarial Practice Textbook Solutions

• Introduction to Corporate Finance Class 12 Secretarial Practice Textbook Solutions
• Sources of Corporate Finance Class 12 Secretarial Practice Textbook Solutions
• Issue of Shares Class 12 Secretarial Practice Textbook Solutions
• Issue of Debentures Class 12 Secretarial Practice Textbook Solutions
• Deposits Class 12 Secretarial Practice Textbook Solutions
• Correspondence with Members Class 12 Secretarial Practice Textbook Solutions
• Correspondence with Debentureholders Class 12 Secretarial Practice Textbook Solutions
• Correspondence with Depositors Class 12 Secretarial Practice Textbook Solutions
• Depository System Class 12 Secretarial Practice Textbook Solutions
• Dividend and Interest Class 12 Secretarial Practice Textbook Solutions
• Financial Market Class 12 Secretarial Practice Textbook Solutions
• Stock Exchange Class 12 Secretarial Practice Textbook Solutions

Introduction to Corporate Finance 12th Secretarial Practice Chapter 1 Solutions Maharashtra Board

Balbharti Maharashtra State Board Class 12 Secretarial Practice Solutions Chapter 1 Introduction to Corporate Finance Textbook Exercise Questions and Answers.

Class 12 Secretarial Practice Chapter 1 Exercise Solutions

1A. Select the correct answer from the options given below and rewrite the statements.

Question 1.
_____________ is related to money and money management.
(a) Production
(b) Marketing
(c) Finance
Answer:
(c) Finance

Question 2.
Finance is the management of _____________ affairs of the company.
(a) monetary
(b) marketing
(c) production
Answer:
(a) monetary

Question 3.
Corporation finance deals with the acquisition and use of _____________ by business corporation.
(a) goods
(b) capital
(c) land
Answer:
(b) capital

Question 4.
Company has to pay _____________ to government.
(a) taxes
(b) dividend
(c) interest
Answer:
(a) taxes

Question 5.
_____________ refers to any kind of fixed assets.
(a) Authorised capital
(b) Issued capital
(c) Fixed capital
Answer:
(c) Fixed capital

Question 6.
_____________ refers to the excess of current assets over current liabilities.
(a) Working capital
(b) Paid-up capital
(c) Subscribed capital
Answer:
(a) Working capital

Question 7.
Manufacturing industries have to invest _____________ amount of funds to acquire fixed assets.
(a) huge
(b) less
(c) minimal
Answer:
(a) huge

Question 8.
When the population is increasing at a high rate, certain manufacturers find this as an opportunity to _____________ business.
(a) close
(b) expand
(c) contract
Answer:
(b) expand

Question 9.
The sum of all _____________ is gross working capital.
(a) expenses
(b) current assets
(c) current liabilities
Answer:
(b) current assets

Question 10.
_____________ means mix up of various sources of funds in desired proportion.
(a) Capital budgeting
(b) Capital structure
(c) Capital goods
Answer:
(b) Capital structure

1B. Match the pairs:

Question 1.

Answer:

Group ‘A’	Group ‘B’
(a) Capital budgeting	(6) Investment decision
(b) Fixed capital	(5) Fixed assets
(c) Working capital	(1) Sum of current assets
(d) Capital structure	(9) Mix up various sources of funds
(e) Corporate finance	(2) Deals with acquisition and use of capital

1C. Write a word or term or a phrase that can substitute each of the following statements:

Question 1.
A key determinant of the success of any business function.
Answer:
Finance

Question 2.
The decision of the finance manager ensures that the firm is well-capitalized.
Answer:
Financing decision

Question 3.
The decision of the finance manager to deploy the funds in a systematic manner.
Answer:
Investment decision

Question 4.
Capital is needed to acquire fixed assets that are used for a longer period of time.
Answer:
Fixed capital

Question 5.
The sum of current assets.
Answer:
Gross working capital

Question 6.
The excess of current assets over current liabilities.
Answer:
Networking capital

Question 7.
The process of converting raw material into finished goods.
Answer:
Production cycle

Question 8.
The boom and recession cycle in the economy.
Answer:
Economic Trend

Question 9.
The ratio of different sources of funds in the total capital.
Answer:
Capital Structure

Question 10.
The internal source of financing.
Answer:
Retained earnings

1D. State whether the following statements are True or False:

Question 1.
Finance is related to money and money management.
Answer:
True

Question 2.
The business firm gives a green signal to the project only when it is profitable.
Answer:
True

Question 3.
Corporate finance brings coordination between various business activities.
Answer:
True

Question 4.
Fixed capital is also referred as circulating capital.
Answer:
False

Question 5.
Working capital stays in the business almost permanently.
Answer:
False

Question 6.
The business will require huge funds if assets are acquired on a lease basis.
Answer:
False

Question 7.
The business dealing in luxurious products will require a huge amount of working capital.
Answer:
True

Question 8.
A firm with large-scale operations will require more working capital.
Answer:
True

Question 9.
Liberal credit policy creates a problem of bad debt.
Answer:
True

Question 10.
Financial institutions and banks cater to the working capital requirement of the business.
Answer:
True

1E. Find the odd one.

Question 1.
Land and Building, Plant and Machinery, Cash.
Answer:
Cash

Question 2.
Debenture Capital, Equity Share Capital, Preference Share Capital.
Answer:
Debenture Capital

Question 3.
Fixed Capital, Capital Structure, Working Capital.
Answer:
Capital Structure

1F. Complete the sentences.

Question 1.
Initial planning of capital requirement is made by _____________
Answer:
entrepreneur

Question 2.
When there is boom in economy, sales will _____________
Answer:
increase

Question 3.
The process of converting raw material into finished goods is called _____________
Answer:
production cycle

Question 4.
During recession period sales will _____________
Answer:
decrease

1G. Select the correct option from the bracket.

Question 1.

(To have the right amount of capital, deploy funds in a systematic manner, fixed capital, working capital, capital structure, carry dividend at a fixed rate)
Answer:

Group ‘A’	Group ‘B’
(a) Financing decision	(1) To have the right amount of capital
(b) Fixed capital	(2) Longer period of time
(c) Investment decision	(3) Deploy funds in a systematic manner
(d) Working capital	(4) Circulating capital
(e) Combination of various sources of funds	(5) capital structure

1H. Answer in one sentence.

Question 1.
Define corporate finance.
Answer:
Corporate finance deals with the raising and using of finance by a corporation.

Question 2.
What is fixed capital?
Answer:
Fixed capital is the capital that is used for buying fixed assets that are used for a longer period of time in the business eg. Capital for plant and machinery etc.

Question 3.
What is working capital?/Define working capital.
Answer:
Working capital is the capital that is used to carry out day-to-day business activities and takes into consideration all current assets of the company.
Eg: for building up inventories.

Question 4.
What is the production cycle?
Answer:
The process of converting raw material into finished goods is called the production cycle.

Question 5.
Define capital structure.
Answer:
Capital structure means to mix up various sources of funds in the desired proportion. To decide capital structure means to decide upon the ratio of different types of capital.

1I. Correct the underlined word and rewrite the following sentences.

Question 1.
Finance is needed to pay dividends to debenture holders.
Answer:
Finance is needed to pay interest to debenture holders.

Question 2.
When there is a recession in the economy sales will increase.
Answer:
When there is a boom in the economy sales will increase.

Question 3.
Share is an acknowledgment of a loan raised by the company.
Answer:
A debenture is an acknowledgment of a loan raised by a company.

Question 4.
Equity shares carry dividends at a fixed rate.
Answer:
Preference shares carry dividends at a fixed rate.

2. Explain the following terms/concepts.

Question 1.
Financing decision
Answer:
A financing decision is a right decision that is made by a finance manager of any corporation ensuring that the firm is well capitalized with the right combination of debt and equity, having access to multiple choices of sources of financing.

Question 2.
Investment decision
Answer:
Investment decisions mean capital budgeting i.e. finding investments and deploying them successfully in the business for greater profits.

Question 3.
Fixed capital
Answer:
Fixed capital is the capital that is used for buying fixed assets that are used for a longer period of time in the business. These assets are not meant for. resale. Examples of fixed capital are capital used for purchasing land and building, furniture, plant, and machinery, etc.

Question 4.
Working Capital
Answer:
Working capital is the capital that is used to carry out day-to-day business activities. It takes into consideration all current assets, of the company. It also refers to ‘Gross Working Capital’.
Examples of working capital are

• for building up inventories.
• for financing receivables.
• for covering day-to-day operating expenses.

3. Study the following case/situation and express your opinion.

1. The management of ‘Maharashtra State Road Transport Corporation’ wants to determine the size of working capital.

Question (a).
Being a public utility service provider will it need less working capital or more?
Answer:
MSRTC being a public utility service provider will need less working capital because of a continuous flow of cash from there, customers thus liabilities are taken care of.

Question (b).
Being a public utility service provider, will it need more fixed capital?
Answer:
Being a public utility service provider MSRTC will need a huge amount of funds to acquire fixed assets thus it will need more fixed capital.

Question (c).
Give one example of a public utility service that you come across on a day-to-day basis.
Answer:
The Indian Railways.

2. A company is planning to enhance its production capacity and is evaluating the possibility of purchasing new machinery whose cost is ₹ 2 crore or has alternative of machinery available on a lease basis.

Question (a).
What type of asset is machinery?
Answer:
Machinery is a Fixed Asset.
A fixed asset may be held for 5, 10 or 20 years and more. But if assets are acquired on a lease or rental basis, then less amount of funds for fixed assets will be needed for business.

Question (b).
Capital used for the purchase of machinery is fixed capital or working capital.
Answer:
Capital used for the purchase of machinery is fixed capital.

Question (c).
Does the size of a business determine the fixed capital requirement?
Answer:
Yes. Where a business firm is set up to carry on large-scale operations, its fixed capital requirements are likely to be high.

4. Distinguish between the following.

Question 1.
Fixed Capital and Working Capital
Answer:

Points	Fixed Capital	Working Capital
1. Meaning	Fixed capital refers to any kind of physical asset, a portion of total capital that is invested in fixed assets.	Working capital refers to the sum of current assets or gross working capital.
2. Nature	It stays in the business almost permanently.	Working capital is circulatory capital. It keeps changing.
3. Purpose	It is invested in fixed assets such as land, building, equipment, etc.	Working capital is invested in short-term assets such as cash, account receivable, inventory, etc.
4. Sources	Fixed capital funding can come from selling shares, debentures, bonds, long-term loans, etc.	Working capital can be funded with short-term loans, deposits, trade credit, etc.
5. Objectives of investors	Investors invest money in fixed capital hoping to make a future profit.	Investors invest money in working capital for getting immediate returns.
6. Risk	Investment in fixed capital implies more risk.	Investment in working capital is less risky. Eg. Land, building, plant and machinery
7. Decisions	Decisions relating to fixed capital investment are generally made by top-level management. Eg. Cash, bills receivable, inventories, cash at the bank	Decisions relating to working capital needs are generally made by middle-level or lower-level management.

5. Answer in brief:

Question 1.
Define capital structure and state its components.
Answer:
Definition: R.H. Wessel “The long term sources of funds employed in a business enterprise.”
John H. Hampton “A firm’s capital structure is the relation between the debt and equity securities that make up the firm’s financing of its assets.” Thus, the term capital structure means security mix. It refers to the proportion of different securities raised by a firm for long-term finance.

Components/Parts of Capital Structure:
There are four basic components of capital structure. They are as follows:
(i) Equity Share Capital:

• It is the basic source of financing activities of the business. Equity share capital is provided by equity shareholders.
• They buy equity shares and help a business firm to raise necessary funds. They bear the ultimate risk associated with ownership.
• Equity shares carry dividends at a fluctuating rate depending upon profit.

(ii) Preference Share Capital:

• Preference shares carry preferential rights as to payment of dividends and have priority over equity shares for return of capital when the company is liquidated.
• These shares carry dividends at a fixed rate.
• They enjoy limited voting rights.

(iii) Retained earnings:

• It is an internal source of financing.
• It is nothing but ploughing back of profit.

(iv) Borrowed capital: It comprises of the following:

• Debentures: A debenture is an acknowledgment of a loan raised by the company. The company has to pay interest at an agreed rate.
• Term Loan: Term loans are provided by the bank and other financial institutions. They carry fixed rate of interest.

Question 2.
State any four factors affecting fixed capital requirements?
Answer:
(i) Nature of business:

• The nature of business certainly plays a role in determining fixed capital requirements. They need to invest a huge amount of money in fixed assets.
• e.g. Rail, road, and other public utility services have large fixed investments.
• Their working capital requirements are nominal because they supply services and not the product.
• They deal in cash sales only.

(ii) Size of business:
The size of a business also affects fixed capital needs. A general rule applies that the bigger the business, the higher the need for fixed capital. The size of the firm, either in terms of its assets or sales, affects the need for fixed capital.

(iii) Scope of business:
Some business firms that manufacture the entire range of their production would require a huge investment in fixed capital. However, those companies that are labour intensive and who do not use the latest technology may require less fixed capital and vice versa.

(iv) Extent of lease or rent:
Companies who take their assets on a lease basis or on a rental basis will require less amount of funds for fixed assets. On the other side, firms that purchase assets will naturally require more fixed capital in the initial stages.

Question 3.
What are Corporate Finance and State’s two decisions which are basic of corporate finance?
OR
Write short note on Corporate Finance
Answer:
Corporate finance deals with the raising and using of finance by a corporation. It includes various financial activities like capital structuring and making investment decisions, financial planning, capital formation, and foreign capital, etc. Even financial organisations and banks play a vital role in corporate financing.

Henry Hoagland expresses, “Corporate Finance deals primarily with the acquisition and use of capital by the business corporation”.

Following two decisions are the basis of corporate finances:
(i) Financing decision:
Every business firm must carefully estimate its capital needs i.e. working capital and fixed capital. The firm needs to mobilize funds from the right sources also maintaining the right combination of debt capital and equity capital. For this balance, a company may go for or raise equity capital or even opt for borrowed funds by way of debentures, public deposits term loans, etc. to raise funds.

(ii) Investment decision:
Once the capital needs are accessed, the finance manager needs to take correct decisions regarding the use of the funds in a systematic manner, productively, using effective cost control measures to generate high profits. Finding investments through proper decisions and using them successfully in business is called ‘capital budgeting

6. Justify the following statements.

Question 1.
The firm has multiple choices of sources of financing.
Answer:

• Business firms require finance in terms of working capital and fixed capital.
• Funds are required at different stages of business.
• The company can raise funds from various sources i.e. from internal and external sources.
• Internal sources could be cash inflows on sales turnover, income from investments, and retained earnings.
• External sources can be obtained for short-term requirements through cash credit, overdraft trade credit, discounting bills of Exchange issues of commercial paper, etc.
• For long-term needs, a firm can meet its financing needs through the issue of shares, debentures, bonds, public deposits, etc. Thus, it is rightly said that the firm has multiple choices of sources of financing.

Question 2.
There are various factors affecting the requirements of fixed capital.
Answer:

• Fixed capital being long-term capital is required for the development and expansion of the company.
• The nature and size of a business have a great impact on fixed capital. Manufacturing businesses require huge fixed capital whereas trading organizations like retailers require less fixed capital.
• Methods of acquiring assets on rentals or on a lease/installment basis will require less amount of fixed assets.
• If fixed assets are available at low prices and concessional rates then it would reduce the need for investment in fixed assets.
• International conditions and economic trends like a boom period will require high investment in fixed assets and a recession will lead to less requirement.
• Similarly, consumer preferences, competition, and highly demanded goods and services will require a large amount of fixed capital. E.g. Mobile phones. Thus, it is rightly said that there are various factors affecting the requirements of fixed capital.

Question 3.
Fixed capital stays in the business almost permanently.
Answer:
Factors determining fixed capital requirements are:

• Fixed capital refers to capital invested for acquiring fixed assets.
• These assets are not meant for resale.
• Fixed capital is capital used for purchasing land and building, furniture, plant, and machinery, etc.
• Such cap al is usually required at the time of the establishment of a new company.
• Existing companies may also need such capital for their expansion and development, replacement of equipment, etc.
• Modern industrial processes require the increased use of heavy automated machinery. Thus, it is rightly said that fixed capital stays in the business almost permanently.

Question 4.
Capital structure is composed of owned funds and borrowed funds.
Answer:

• Capital structure means to mix up of various sources of funds in desired proportions.
• To decide capital structures means to decide upon the ratio of different types of capital.
• A firm’s capital structure is the relation between the debt and equity securities that make up the firm’s financing of its assets.
• The capital structure is composed of own funds which include share capital, free serves, and surplus, and borrowed funds which represent debentures, bank loans, and long-term loans provided by financial institutions.
• Thus capital structure = Equity share capital + preference share capital + reserves + debentures.
• Thus, it is rightly said that capital structure is composed of owned funds and borrowed funds.

Question 5.
There are various factors affecting the requirement of working capital.
Answer:

• The nature and size of a business affect the requirement of working capital. Trading or merchandising firms and big retail enterprises need a large amount of capital compared to small firms which need a small amount of working capital.
• If the period of the production cycle is longer then the firm needs more amount of working capital. If the manufacturing cycle is short, it requires less working capital.
• During the boom period sales will increase leading to increased investment in stocks, thus requiring additional working capital and during the recession, it is vice versa.
• Along with the expansion and growth of the firm or company in terms of sales and fixed assets, the requirement of working capital increases.
• If there is proper coordination, communication, and co-operation between production and sales departments then the requirement of working capital is less.
• A liberal credit policy increases the possibility of bad debts and in such cases, the requirement of working capital is high, whereas a firm making cash sales requires less working capital.

7. Answer the following questions.

Question 1.
Discuss the importance of Corporate Finance?
Answer:
Corporate finance deals with the raising and utilizing of finance by a corporation. It also deals with capital structuring and making investment decisions, financial planning of capital, and the money market. The finance manager should ensure that:
The firm has adequate finance and it’s being utilized effectively;
Generate minimum return for its owners.

The importance of Corporate Finance are as follows:
(i) Helps in decision making:
Most important decisions of business enterprises are made on the basis of availability of funds, as without finance any function of business enterprise is difficult to be performed independently. Obtaining the funds from the right sources at a lower cost and productive utilization of funds would lead to higher profits. Thus corporate finance plays a significant role in the decision-making process.

(ii) Helps in raising capital for a project:
A new business venture needs to raise capital. Business firms can raise funds by issuing shares, debentures, bonds or even by taking loans from the banks.

(iii) Helps in Research and Development
Research and Development need to be undertaken by firms for growth and expansion of business and to enjoy a competitive advantage. Research and development mostly involve lengthy and detailed technical work for the execution of projects. Through surveys and market analysis etc. companies may have to upgrade old products or develop new products to face competition and attract consumers. Thus the availability of adequate finance helps to generate high efficiency.

(iv) Helps in the smooth running of the business firm:
A smooth flow of corporate finance is important to pay the salaries of employees on time, pay loans, and purchase the required raw materials. At the same time finance is needed for sales promotion of existing products and more so for the launch of new products effectively.

(v) Brings co-ordination between various activities:
Corporate finance plays a significant role in the coordination and control of all activities in an organization. Production activity requires adequate finance for the purchase of raw materials and meeting other day-to-day financial requirements for the smooth running of the production unit. If the production increases, sales will also increase by contributing the income of the concern and profit to increase.

(vi) Promotes expansion and diversification:
Corporate finance provides money for the purchase of modern machines and sophisticated technology. Modern machines and technology help to improve the performance of the firm in terms of profits. It also helps the firm to expand and diversify the business.

(vii) Managing risk:
Companies have to manage several risks such as sudden fall in sales, loss due to natural calamity, loss due to workers strikes, change in government policies, etc. Financial aids help in such situations to manage such risks.

(viii) Replace old assets:
Assets like plants and machinery have become old and outdated over the years. Finance is required to purchase new assets or replace the old assets with new assets having new technology and features.

(ix) Payment of dividend and interest:
Finance is needed to pay the dividend to shareholders, interest to creditors, bank, etc.

(x) Payment of taxes/fees:
The company has to pay taxes to the government such as Income tax, Goods and Service Tax (GST), and fees to the Registrar of Companies on various occasions. Finance is needed for paying these taxes and fees.

Question 2.
Discuss the factors determining working capital requirements?
Answer:
Working Capital = Current Assets – Current Liabilities.
In other words, it is also called ‘Circulating Capital’. Also, refer to ‘GROSS WORKING CAPITAL.’ Management needs to determine the size of working capital with reference to the economic environment and other aspects within the business firm.

Factors determining/influencing working capital requirements are as follows:
(i) Nature of Business:
The working capital requirements are highly influenced by the nature of the business. Trading/ merchandising forms concerned with the distribution of goods require a huge amount of working capital to maintain a large stock of the variety of goods to meet customers’ demands are extend credit facilities to attract them. Whereas public utility concerns have to maintain small working capital because of a continuous flow of cash from their customers.

(ii) Size of business:
The size of a business also affects the requirements of working capital. Size of the firm refers to the scale of operation i.e. a firm with large scale operations will require more working capital and vice versa.

(iii) Volume of Sales:
The volume of sales and the size of the working capital have a direct relationship with each other. If the volume of sales increases there is an increase in the amount of working capital.

(iv) Production cycle:
The process of converting raw material into finished goods is called the ‘production cycle’. If the production cycle period is longer, the firm needs more amount of working capital. If the manufacturing cycle is short, it requires less working capital.

(v) Business cycle:
When there is a boom in the economy, sales will increase resulting in to increase in investment in stock. This will require additional working capital. During a recession period, sales will decline and consequently, the need for working capital will also decrease.

(vi) Terms of purchases and sales:
If credit terms of purchase are favourable and terms of sales are less liberal, then the requirement of cash will be less. Thus, the working capital requirement will be reduced.
A firm that enjoys more credit facilities needs less working capital. On the other hand, if a firm does not get proper credit for purchases and adopts a liberal credit policy for sales if requires more working capital.

(vii) Credit Control:
Credit control includes the factors such as volume of credit sales, the terms of credit sales, the collection policy etc. A firm with a good credit control policy will have more cash flow reducing the working capital requirement. Whereas if the firm’s credit policy is liberal there would be more requirements of the working capital.

(viii) Growth and Expansion:
Those firms which are growing and expanding at a rapid pace need more working capital compared to those firms which are stable in their growth.

(ix) Management ability:
The requirement of working capital is reduced if there is proper coordination in the production and distribution of goods. A firm stocking on heavy inventory calls for a higher level of working capital.

(x) External factors:
If the financial institutions and banks provide funds to the firm as and when required, the need for working capital is reduced.

Maharashtra State Board 12th Std Secretarial Practice Textbook Solutions

• Introduction to Corporate Finance Class 12 Secretarial Practice Textbook Solutions
• Sources of Corporate Finance Class 12 Secretarial Practice Textbook Solutions
• Issue of Shares Class 12 Secretarial Practice Textbook Solutions
• Issue of Debentures Class 12 Secretarial Practice Textbook Solutions
• Deposits Class 12 Secretarial Practice Textbook Solutions
• Correspondence with Members Class 12 Secretarial Practice Textbook Solutions
• Correspondence with Debentureholders Class 12 Secretarial Practice Textbook Solutions
• Correspondence with Depositors Class 12 Secretarial Practice Textbook Solutions
• Depository System Class 12 Secretarial Practice Textbook Solutions
• Dividend and Interest Class 12 Secretarial Practice Textbook Solutions
• Financial Market Class 12 Secretarial Practice Textbook Solutions
• Stock Exchange Class 12 Secretarial Practice Textbook Solutions

Insurance and Annuity Class 12 Commerce Maths 2 Chapter 2 Miscellaneous Exercise 2 Answers Maharashtra Board

Balbharati Maharashtra State Board 12th Commerce Maths Digest Pdf Chapter 2 Insurance and Annuity Miscellaneous Exercise 2 Questions and Answers.

Std 12 Maths 2 Miscellaneous Exercise 2 Solutions Commerce Maths

(I) Choose the correct alternative.

Question 1.
“A contract that pledges payment of an agreed-upon amount to the person (or his/her nominee) on the happening of an event covered against” is technically known as
(a) Death coverage
(b) Saving for future
(c) Life insurance
(d) Provident fund
Answer:
(c) Life insurance

Question 2.
Insurance companies collect a fixed amount from their customers at a fixed interval of time. This amount is called
(a) EMI
(b) Installment
(c) Contribution
(d) Premium
Answer:
(d) Premium

Question 3.
Following are different types of insurance.
I. Life insurance
II. Health insurance
III. Liability insurance
(a) Only I
(b) Only II
(c) Only III
(d) All the three
Answer:
(d) All the three

Question 4.
By taking insurance, an individual
(a) Reduces the risk of an accident
(b) Reduces the cost of an accident
(c) Transfers the risk to someone else
(d) Converts the possibility of large loss to the certainty of a small one
Answer:
Converts the possibility of large loss to the certainty of a small one

Question 5.
You get payments of ₹ 8,000 at the beginning of each year for five years ta 6%, what is the value of this annuity?
(a) ₹ 34,720
(b) ₹ 39,320
(c) ₹ 35,720
(d) ₹ 40,000
Answer:
(c) ₹ 35,720

Question 6.
In an ordinary annuity, payments or receipts occur at
(a) Beginning of each period
(b) End of each period
(c) Mid of each period
(d) Quarterly basis
Answer:
(b) End of each period

Question 7.
The amount of money today which is equal to a series of payments in the future is called
(a) Normal value of the annuity
(b) Sinking value of the annuity
(c) Present value of the annuity
(d) Future value of the annuity
Answer:
(c) Present value of the annuity

Question 8.
Rental payment for an apartment is an example of
(a) Annuity due
(b) Perpetuity
(c) Ordinary annuity
(d) Installment
Answer:
(b) Perpetuity

Question 9.
_________ is a series of constant cash flows over a limited period of time.
(a) Perpetuity
(b) Annuity
(c) Present value
(d) Future value
Answer:
(b) Annuity

Question 10.
A retirement annuity is particularly attractive to someone who has
(a) A severe illness
(b) Risk of low longevity
(c) Large family
(d) Chance of high longevity
Answer:
(d) Chance of high longevity

(II) Fill in the blanks.

Question 1.
An installment of money paid for insurance is called _________
Answer:
premium

Question 2.
General insurance covers all risks except _________
Answer:
life

Question 3.
The value of insured property is called _________
Answer:
property value

Question 4.
The proportion of property value to insured is called _________
Answer:
policy value

Question 5.
The person who receive annuity is called _________
Answer:
Annuitant

Question 6.
The payment of each single annuity is called _________
Answer:
installment

Question 7.
The intervening time between payment of two successive installments is called as _________
Answer:
payment period

Question 8.
An annuity where payments continue forever is called _________
Answer:
perpetuity

Question 9.
If payments of an annuity fall due at the beginning of every period, the series is called _________
Answer:
annuity due

Question 10.
If payments of an annuity fall due at the end of every period, the series is called annuity _________
Answer:
immediate

(III) State whether each of the following is True or False.

Question 1.
General insurance covers life, fire, and theft.
Answer:
False

Question 2.
The amount of claim cannot exceed the amount of loss.
Answer:
True

Question 3.
Accident insurance has a period of five years.
Answer:
False

Question 4.
Premium is the amount paid to the insurance company every month.
Answer:
True

Question 5.
Payment of every annuity is called an installment.
Answer:
False

Question 6.
Annuity certainly begins on a fixed date and ends when an event happens.
Answer:
True

Question 7.
Annuity contingent begins and ends on certain fixed dates.
Answer:
False

Question 8.
The present value of an annuity is the sum of the present value of all installments.
Answer:
True

Question 9.
The future value of an annuity is the accumulated value of all installments.
Answer:
False

Question 10.
The sinking fund is set aside at the beginning of a business.
Answer:
True

(IV) Solve the following problems.

Question 1.
A house valued at ₹ 8,00,000 is insured at 75% of its value. If the rate of premium is 0.80%. Find the premium paid by the owner of the house. If the agent’s commission is 9% of the premium, find the agent’s commission.
Solution:
Property value = ₹ 8,00,000
Policy value = 75% × 8,00,000 = ₹ 6,00,000
∵ Rate of Premium = 0.80%
∴ Amount of Premium = 0.80% × 6,00,000 = ₹ 4,800
∵ Rate of commission = 9%
∴ Agent commission = 9% × 4800 = ₹ 432

Question 2.
A shopkeeper insures his shop and godown are valued at ₹ 5,00,000 and ₹ 10,00,000 respectively for 80% of their values. If the rate of premium is 8%, find the total annual premium.
Solution:
Property value of shop = ₹ 5,00,000
∴ Policy value = 80% × 5,00,000 = ₹ 4,00,000
∵ Rate of Premium = 8%
∴ Amount of premium = 8% × 4,00,000 = ₹ 32,000
∵ Property value of Godown = ₹ 10,00,000
∴ Policy value = 80% × 10,00,000 = ₹ 8,00,000
∵ Rate of Premium = 8%
∴ Amount of Premium = 8% × 8,00,000 = ₹ 64,000
∴ Total annual Premium = 64,000 + 32,000 = ₹ 96,000

Question 3.
A factory building is insured for \(\left(\frac{5}{6}\right)^{\text {th }}\) of its value at a rate of premium of 2.50%. If the agent is paid a commission of ₹ 2,812.50, which is 7.5% of the premium, find the value of the building.
Solution:
Let the Property value be ₹ x
∴ Policy value = ₹ \(\frac{5 x}{6}\)
∵ Rate of premium = 2.50%
∴ Amount of premium = \(\frac{5 x}{6}\) × 2.50% = ₹ \(\frac{x}{48}\)
∵ Rate of Agent commission = 7.5%
∴ Agent commission = 7.5% × \(\frac{x}{48}\)
∴ 2812.50 = \(\frac{x}{640}\)
∴ 2812.50 × 640 = x
∴ x = ₹ 18,00,000
∴ Value of the building is ₹ 18,00,000.

Question 4.
A merchant takes a fire insurance policy to cover 80% of the value of his stock. Stock worth ₹ 80,000 was completely destroyed in a fire. While the rest of the stock was reduced to 20% of its value. If the proportional compensation under the policy was ₹ 67,200, find the value of the stock.
Solution:
Let the Property value be ₹ x
∴ Policy value 80% × x = ₹ \(\frac{4 x}{5}\)
∵ Complete loss = ₹ 80,000
∴ Partial loss = 20% × (x – 8,00,000) = \(\frac{x-80,000}{5}\)
∴ Total loss = 80,000 + \(\frac{x-80,000}{5}\) = \(\frac{x}{5}\) + 64,000
∵ Claim = ₹ 67,200

∴ x = ₹ 1,00,000
∴ The value of the stock is ₹ 1,00,000.

Question 5.
A 35-year old person takes a policy for ₹ 1,00,000 for a period of 20 years. The rate of premium is ₹ 76 and the average rate of bonus is ₹ 7 per thousand p.a. If he dies after paying 10 annual premiums, what amount will his nominee receive?
Solution:
Policy value = ₹ 1,00,000
Period of Policy = 20 years
∵ Rate of premium = ₹ 76 per thousand
∴ Amount of premium = \(\frac{76}{1,000}\) × 1,00,000 = ₹ 7,600
∴ Total Premium = 7,600 × 10 = ₹ 76,000
∴ Rate of Bonus = ₹ 7 per thousand p.a
∴ Total Bonus = \(\frac{7}{1,000}\) × 1,00,000 = ₹ 7,000
∴ Amount received by Nominee = Policy value + Bonus earned
= 1,00,000 + 7,000
= ₹ 1,07,000

Question 6.
15,000 articles costing ₹ 200 per dozen were insured against fire for ₹ 1,00,000. If 20% of the articles were burnt completely and 2,400 other articles were damaged to the extent of 80% of their value, find the amount that can be claimed under the policy.
Solution:
Total Articles = 15,000
∴ Property value = \(\frac{15,000}{12}\) × 200 = 2,50,000
∵ Policy value = ₹ 1,00,000
∴ Complete loss = 20% × 2,50,000 = ₹ 50,000
∴ Partial loss = 80% × \(\frac{2,400}{12}\) × 200 = ₹ 3,20,000
∴ Total loss = 32,000 + 50,000 = ₹ 82,000
∴ Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss
= \(\frac{1,00,000}{2,50,000}\) × 82,000
= ₹ 32,800

Question 7.
For what amount should a cargo worth ₹ 25,350 be insured so that in the event of a total loss, its value, as well as the cost of insurance, may be recovered when the rate of premium is 2.5%.
Solution:
Let the policy value be ₹ 100 which includes the cost of insurance and premium
∴ Property value = 100 – 2.50 = ₹ 97.50
If the value of the cargo is ₹ 97.50, then the policy value is ₹ 100.
If the value of the cargo is ₹ 25,350, then
Policy value = \(\frac{100 \times 25,350}{97.50}\) = ₹ 26,000

Question 8.
A cargo of grain is insured at \(\left(\frac{3}{4}\right)\)% to cover 70% of its value. ₹1,008 is the amount of premium paid. If the grain is worth ₹ 12 per kg, how many kg of the grain did the cargo contain?
Solution:
Let the Property value be ₹ x
∴ policy value = 70% × x = ₹ \(\frac{7 x}{10}\)
∵ Rate of premium = \(\frac{3}{4}\)%
∴ Amount of premium = Rate × Policy value

∴ x = ₹ 1,92,000
∵ Rate of Jowar = ₹ 12/kg
∴ Quantity of Jowar = \(\frac{1,92,000}{12}\) = 16,000 kgs

Question 9.
4,000 bedsheets worth ₹ 6,40,000 were insured for \(\left(\frac{3}{7}\right)^{t h}\) of their value. Some of
the bedsheets were damaged in the rainy season and were reduced to 40% of their value. If the amount recovered against damage was ₹ 32,000. Find the number of damaged bedsheets.
Solution:
∵ Property value = ₹ 6,40,000
∴ Policy value = 6,40,000 × \(\frac{3}{7}\) = ₹ \(\frac{19,20,000}{7}\)
∴ Cost of one Bedsheet = \(\frac{6,40,000}{4,000}\) = ₹ 160
Let ‘x’ bedsheets be damaged.
∴ Cost of x bedsheets = ₹ 160x

∴ 875 Bedsheets damaged.

Question 10.
A property valued at ₹ 7,00,000 is insured to the extent of ₹ 5,60,000 at \(\left(\frac{5}{8}\right)\)% less 20%. Calculate the saving made in the premium. Find the amount of loss that the owner must bear, including premium, if the property is damaged to the extent of 40% of its value.
Solution:
∵ Property value = ₹ 7,00,000
∵ Policy value = ₹ 5,60,000
∵ Rate of premium = \(\frac{5}{8}\)%
∴ Amount of premium = \(\frac{5}{8}\)% × 5,60,000 = ₹ 3,500
New rate of premium = \(\frac{5}{8}\)% less 20%
= \(\frac{5}{8}\) – [20% x \(\frac{5}{8}\)]
= \(\frac{5}{8}\) – \(\frac{1}{8}\)
= \(\frac{1}{2}\)%
∴ Amount of premium = \(\frac{1}{2}\)% × 5,60,000 = ₹ 2,800
∴ Saving made in premium = 3,500 – 2,800 = ₹ 700
∴ Loss = 7,00,000 × 40% = 2,80,000
∴ Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss
= \(\frac{5,60,000}{7,00,000}\) × 2,80,000
= ₹ 2,24,000
∴ Loss bear by owner = loss – claim + premium
= 2,80,000 – 2,24,000 + 2,800
= ₹ 58,800

Question 11.
Stocks in a shop and godown worth ₹ 75,000 and ₹ 1,30,000 respectively were insured through an agent who receive 15% of the premium as commission. If the shop was insured for 80% and godown for 60% of the value, find the amount of agent’s commission when the premium was 0.80% less 20%. If the entire stock in the shop and 20% stock in the godown is destroyed by fire, find the amount that can be claimed under the policy.
Solution:
∵ Rate of premium = 0.80% less 20%
= 0.80 – 20% × 0.80
= 0.80 – 0.16
= 0.64%
For Shop
∵ Property value = ₹ 75,000
∴ Policy value = 80% × 75,000 = ₹ 60,000
∴ Premium = 0.64% × 60,000 = ₹ 384
∵ Loss = ₹ 75,000
∵ Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss
= \(\frac{60,000}{75,000}\) × 75,000
= ₹ 60,000
For Godown
∵ Property value = ₹ 1,30,000
∴ Policy value = 60% × 1,30,000 = ₹ 78,000
∴ Premium = 0.64% × 78,000 = ₹ 499.2
Loss = 20% × 1,30,000 = ₹ 26,000
∴ Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss
= \(\frac{78,000}{1,30,000}\) × 26,000
= ₹ 15,600
Total claim = 16,600 + 60,000 = ₹ 75,600
∵ Rate of commission = 15%
∴ Agent commission = 15% × [384 + 499.2]
= 15% × 883.2
= ₹ 132.48

Question 12.
A person holding a life policy of ₹ 1,20,000 for a term of 25 years wants to discontinue after paying a premium for 8 years at the rate of ₹ 58 per thousand p.a. Find the amount of paid-up value he will receive on the policy. Find the amount he will receive if the surrender value granted is 35% of the premium paid, excluding the first year’s premium.
Solution:
Policy value = ₹ 1,20,000
∵ Rate of premium = ₹ 58 per thousand p.a.
∴ Premium for 8 years = \(\frac{8 \times 58}{1000}\) × 1,20,000 = ₹ 55,680
∴ Amount of 1st premium = \(\frac{55,680}{8}\) = ₹ 6,960
∵ Paid-up value of policy = \(\frac{\text { No of Premium paid }}{\text { Terms of policy }}\) × Policy value
= \(\frac{8}{25}\) × 1,20,000
= ₹ 38,400
∵ Surrender value = 35% × [Total premium – 1st year premium]
= 35% × [55,680 – 6,960]
= 35% × 48,720
= ₹ 17,052

Question 13.
A godown valued at ₹ 80,000 contained stock worth ₹ 4,80,000. Both were insured against fire. Godown for ₹ 50,000 and stock for 80% of its value. A part of stock worth ₹ 60,000 was completely destroyed and the rest was reduced to 60% of its value. The amount of damage to the godown is ₹ 40,000. Find the amount that can be claimed under the policy.
Solution:
For Godown
∵ Property value = ₹ 80,000
∵ Policy value = ₹ 50,000
∵ Loss = ₹ 40,000
∵ Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss
= \(\frac{50,000}{80,000}\) × 40,000
= ₹ 25,000
For stock
∵ Property value = ₹ 4,80,000
∵ Policy value = 80% × 4,80,000 = ₹ 3,84,000
∵ Complete loss = ₹ 60,000
∴ Partial loss = (100 – 60)% × [4,80,000 – 60,000]
= 40% × 4,20,000
= ₹ 1,68,000
∴ Total loss = 1,68,000 + 60000 = ₹ 2,28,000
∴ Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss
= \(\frac{3,84,000}{4,80,000}\) × 2,28,000
= ₹ 1,82,400
∴ Total claim = 25,000 + 1,82,400 = ₹ 2,07,400

Question 14.
Find the amount of an ordinary annuity if a payment of ₹ 500 is made at the end of every quarter for 5 years at the rate of 12% per annum compounded quarterly. [Given: (1.03)²⁰ = 1.8061]
Solution:
∵ C = ₹ 500
∵ r = 12% p.a. compounded quarterly,
∴ r = \(\frac{12}{4}\) = 3%
∵ n = 5 years
But, payment is made quarterly
∴ n = 5 × 4 = 20

Question 15.
Find the amount a company should set aside at the end of every year if it wants to buy a machine expected to cost ₹ 1,00,000 at the end of 4 years and interest rate is 5% p.a. compounded annually.
Solution:
∵ A = ₹ 1,00,000
∵ r = 5% p.a.
∴ i = \(\frac{r}{100}=\frac{5}{100}\) = 0.05
∵ n = 4 years
∵ A = \(\frac{C}{i}\left[(1+\mathrm{i})^{n}-1\right]\)
∴ 1,00,000 = \(\frac{C}{0.05}\)[(1 + 0.05)⁴ – 1]
∴ 1,00,000 × 0.05 = C [(1.05)⁴ – 1]
∴ 5,000 = C(1.2155 – 1)
∴ 5,000 = C × 0.2155
∴ \(\frac{5,000}{0.2155}\) = C
∴ C = ₹ 23,201.86

Question 16.
Find the least number of years for which an annuity of ₹ 3,000 per annum must run in order that its amount exceeds ₹ 60,000 at 10%compounded annually. [Given: (1.1)¹¹ = 2,8531, (1.1)¹² = 3.1384]
Solution:
∵ A = ₹ 60,000
∵ C = ₹ 3,000
∵ r = 10% p.a.
∴ i = \(\frac{r}{100}=\frac{10}{100}\) = 0.1
∵ A = \(\frac{C}{i}\left[(1+i)^{n}-1\right]\)
∴ 60,000 = \(\frac{3,000}{0.1}\left[(1+0.1)^{n}-1\right]\)
∴ 60,000 = 30,000[(1.1)ⁿ – 1]
∴ \(\frac{60,000}{30,000}\) + 1 = (1.1)ⁿ
∴ 2 + 1 = (1.1)ⁿ
∴ 3 = (1.1)ⁿ
Taking log
∴ log 3 = log (1.1)ⁿ
∴ log 3 = n log(1.1)
∴ \(\frac{\log 3}{\log 1.1}\) = n
∴ n = \(\frac{0.4771}{0.0414}\) = 11.52 ~ 12 years

Question 17.
Find the rate of interest compounded annually if an ordinary annuity of ₹ 20,000 per year amounts to ₹ 41,000 in 2 years.
Solution:
∵ C = ₹ 20,000
∵ A = ₹ 41,000
∵ n = 2 years

∴ r = 5% p.a.

Question 18.
A person purchases a television by paying ₹ 20,000 in cash and promising to pay ₹ 1,000 at the end of every month for the next 2 years. If money is worth 12% p.a., converted monthly. Find the cash price of the television. [Given: (1.01)^-24 = 0.7880]
Solution:
Down payment = ₹ 20,000
∵ n = 2 years
But, EMI Payable monthly
∴ n = 2 × 12 = 24
∵ r = 12% p.a. compounded monthly

∴ P = 1,00,00 × 0.2120
∴ P = ₹ 21,200
Cash price = Present value + Down payment
= 21,200 + 20,000
= ₹ 41,200

Question 19.
Find the present value of an annuity immediate of ₹ 20,000 per annum for 3 years at 10% p.a. compounded annually. [Given: (1.1)^-3 = 0.7513]
Solution:
∵ C = ₹ 20,000
∵ n = 3 years
∵ r = 10% p.a.

∴ P = 2,00,000 [1 – 0.7513]
∴ P = 2,00,000 [0.2487]
∴ P = ₹ 49,740

Question 20.
A man borrowed some money and paid it back in 3 equal installments of ₹ 2,160 each. What amount did he borrow if the rate of interest was 20% per annum compounded annually? Also, find the total interest charged. [Given: (1.2)^-3 = 0.5788]
Solution:
∵ C = ₹ 2,160
∵ n = 3
∵ r = 20% p.a.

∴ P = ₹ 6,251.04
∴ Total amount paid = 2,160 × 3 = ₹ 6,480
∴ Interest = 6,480 – 6,251.04 = ₹ 228.96

Question 21.
A company decides to set aside a certain amount at the end of every year to create a sinking fund that should amount to ₹ 9,28,200 in 4 years at 10% p.a. Find the amount to be set aside every year. [Given: (1.1)⁴ = 1.4641]
Solution:
∵ A = ₹ 9,28,200
∵ n = 4 years
∵ r = 10% p.a.

∴ 9,28,200 × 0.1 = C[1.4641 – 1]
∴ 92,820 = C × 0.4641
∴ \(\frac{92,820}{0.4641}\) = C
∴ C = ₹ 2,00,000

Question 22.
Find the future value after 2 years if an amount of ₹ 12,000 is invested at the end of every half-year at 12% p.a. compounded half-yearly. [Given: (1.06)⁴ = 1.2625]
Solution:
∵ n = 2 years
Payable half yearly, n = 2 × 2 = 4
∵ C = ₹ 12,000
∵ r = 12% p.a. Compounded half yearly


∴ A = 1,00,000 [1.2625 – 1]
∴ A = 1,00,000 × 0.2625
∴ A = ₹ 26,250

Question 23.
After how many years would an annuity due of ₹ 3,000 p.a. accumulated ₹ 19,324.80 at 20% p.a. compounded annually? [Given: (1.2)⁴ = 2.0736]
Solution:
∵ C = ₹ 3,000
∵ A = ₹ 9,324.80
∵ r = 20% p.a.

∴ 19,324.80 = 15,000 × 1.2[(1.2)ⁿ – 1]
∴ 19,324.80 = 18,000[(1.2)ⁿ – 1]
∴ \(\frac{19,324.80}{18,000}\) + 1 = (1.2)ⁿ
∴ 1.0736 + 1 = (1.2)ⁿ
∴ 2.0736 = (1.2)ⁿ
∴ (1.2)⁴ = (1.2)ⁿ
∴ n = 4 years

Question 24.
Some machinery is expected to cost 25% more over its present cost of ₹ 6,96,000 after 20 yeas. The scrap value of the machinery will realize ₹ 1,50,000. What amount should be set aside at the end of every year at 5% p.a. compound interest for 20 years to replace the machinery? [Given: (1.05)²⁰ = 2655]
Solution:
Present cost = ₹ 6,96,000
Expected cost = 25% × 6,96,000 + 6,96,000
= 1,74,000 + 6,96,000
= ₹ 8,70,000
∴ Scrap value = ₹ 1,50,000
∴ Sinking fund = 8,70,000 – 1,50,000 = ₹ 7,20,000
∴ A = ₹ 7,20,000, n = 20 years, r = 5% p.a.

∴ 7,20,000 × 0.05 = C[(1.05)²⁰ – 1]
∴ 36,000 = C[2.655 – 1]
∴ 36,000 = C × 1.655
∴ \(\frac{36,000}{1.655}\) = C
∴ C = ₹ 21,752.27

12th Commerce Maths Digest Pdf

• 12th Commerce Maths Exercise 2.1 Solutions
• 12th Commerce Maths Exercise 2.2 Solutions
• 12th Commerce Maths Miscellaneous Exercise 2 Solutions

Insurance and Annuity Class 12 Commerce Maths 2 Chapter 2 Exercise 2.2 Answers Maharashtra Board

Balbharati Maharashtra State Board 12th Commerce Maths Digest Pdf Chapter 2 Insurance and Annuity Ex 2.2 Questions and Answers.

Std 12 Maths 2 Exercise 2.2 Solutions Commerce Maths

Question 1.
Find the accumulated (future) value of annuity of ₹ 800 for 3 year at interest rate 8% compounded annually. [Given: (1.08)³ = 1.2597]
Solution:
∵ C = ₹ 800
∵ n = 3 years
∵ r = 8% p.a.

∴ A = 10,000[(1.08)³ – 1]
∴ A = 10,000[1.2597 – 1]
∴ A = 10,000 × 0.2597
∴ A = ₹ 2,597

Question 2.
A person invested ₹ 5,000 every year in finance company that offered him interest compounded at 10% p.a., what is the amount accumulated after 4 years? [Given: (1.1)⁴ = 1.4641]
Solution:
∵ C = ₹ 5,000
∵ r = 10% p.a.

= 50,000[(1.1)⁴ – 1]
= 50,000[1.4641 – 1]
= 50,000 × 0.4641
= ₹ 23,205

Question 3.
Find the amount accumulated after 2 years if a sum of ₹ 24,000 is invested every six months at 12% p.a. compounded half yearly. [Given: (1.06)⁴ = 1.2625]
Solution:
∵ C = ₹ 24,000
∵ n = 2 years
But invested half yearly
∴ n = 2 × 2 = 4
∵ r = 12% p.a. compounded half yearly

= 4,00,000[(1.06)⁴ – 1]
= 4,00,000[1.2625 – 1]
= 4,00,000 × 0.2625
= ₹ 1,05,000

Question 4.
Find the accumulated value after 1 year of an annuity immediate in which ₹ 10,000 are invested every quarter at 16% p.a. compounded quarterly. [Given: (1.04)⁴ = 1.1699]
Solution:
∵ C = ₹ 10,000
∵ n = 1 year
But invested every quarterly
∴ n = 1 × 4 = 4
∴ r = 16% p.a. compounded quarterly

= 2,50,000 [1.1699 – 1]
= 2,50,000 × 0.1699
= ₹ 42,475

Question 5.
Find the present value of an annuity immediate of ₹ 36,000 p.a. for 3 years at 9% p.a. compounded annually. [Given: (1.09)^-3 = 0.7722]
Solution:
∵ C = ₹ 36,000
∵ n = 3 years
∵ r = 9% p.a.

= 4,00,000 × 0.2278
= ₹ 91,120

Question 6.
Find the present value of ordinary annuity of ₹ 63,000 p.a. for 4 years at 14% p.a. compounded annually. [Given: (1.14)^-4 = 0.5921]
Solution:
∵ C = ₹ 63,000
∵ n = 4 years
∵ r = 14% p.a.

= 4,50,000[1 – 0.5921]
= 4,50,000 × 0.4079
= ₹ 1,83,555

Question 7.
A lady plans to save for her daughter’s marriage. She wishes to accumulate a sum of ₹ 4,64,100 at the end of 4 years. What amount should she invest every year if she get an interest of 10%p.a. compounded annually? [Given: (1.1)⁴ = 1.4641]
Solution:
∵ A = ₹ 4,64,100
∵ n = 4 years
∵ r = 10% p.a.

∴ 46,410 = C[1.4641 – 1]
∴ 46,410 = C × 0.4641
∴ \(\frac{46,410}{0.4641}\) = C
∴ C = ₹ 1,00,000

Question 8.
A person wants to create a fund of ₹ 6,96,150 after 4 years at the time of his retirement. He decides to invest a fixed amount at the end of every year in a bank that offers him interest of 10% p.a. compounded annually. What amount should he invest every year? [Given: (1.1)⁴ = 1.4641]
Solution:
∵ A = ₹ 6,96,150
∵ n = 4 years
∵ r = 10% p.a

∴ 69,615 = C[1.4641 – 1]
∴ 69,615 = C × 0.4641
∴ \(\frac{69,615}{0.4641}\) = C
∴ C = ₹ 1,50,000

Question 9.
Find the rate of interest compounded annually if an annuity immediate at ₹ 20,000 per year amounts to ₹ 2,60,000 in 3 years.
Solution:
∵ C = ₹ 20,000
∵ A = ₹ 2,60,000
∵ n = 3 years

∴ 13i = 3i + 3 i² + i³
∴ 13i = i(3 + 3i + i²)
∴ 13 = 3 + i + i²
∴ i² + 3i + 3 – 13 = 0
∴ i² + 3i – 10 = 0
∴ (i + 5) (i – 2) = 0
∴ i + 5 = 0 or i – 2 = 0
∴ i = -5 or i = 2
∵ Rate of interest cannot be negative
∴ i = 2 is accepted
∴ \(\frac{r}{100}\) = 2
∴ r = 200% p.a.

Question 10.
Find the number of years for which an annuity of ₹ 500 is paid at the end of every years, if the accumulated amount works out to be ₹ 1,655 when interest is compounded annually at 10% p.a.
Solution:
∵ C = 7500
∵ A = 71,655
∵ r = 10% p.a.


∴ 0.331 + 1 = (1.1)ⁿ
∴ 1.331 = (1.1)ⁿ
∴ (1.1)³ = (1.1)ⁿ
∴ n = 3 years

Question 11.
Find the accumulated value of annuity due of ₹ 1,000 p.a. for 3 years at 10% p.a. compounded annually. [Given: (1.1)³ = 1.331]
Solution:
∵ C = ₹ 1,000
∵ n = 3 years
∵ r = 10% p.a.

∴ A’ = 10,000 × 1.1[(1.1)³ – 1]
∴ A’ = 11,000 [1.331 – 1]
∴ A’ = 11,000 × 0.331
∴ A’ = ₹ 3,641

Question 12.
A person plans to put ₹ 400 at the beginning of each year for 2 years in a deposit that gives interest at 2% p.a. compounded annually. Find the amount that will be accumulated at the end of 2 years. [Given: (1.02)² = 1.0404]
Solution:
∵ C = ₹ 400
∵ r = 2% p.a.


= 20,000 (1.02) (1.0404 – 1)
= 20,400 [0.0404]
= ₹ 824.16

Question 13.
Find the present value of an annuity due of ₹ 600 to be paid quarterly at 32% p.a. compounded quarterly. [Given (1.08)^-4 = 0.7350]
Solution:
∵ C = ₹ 600
∵ n = 1 year
∴ But invested every quarterly
∴ n = 1 × 4 = 4
∵ r = 32% p.a. compounded quarterly

= 7,500(1.08) [1 – 0.7350]
= 8,100 [0.2650]
= ₹ 2,146.5

Question 14.
An annuity immediate is to be paid for some years at 12% p.a. The present value of the annuity is ₹ 10,000 and the accumulated value is ₹ 20,000. Find the amount of each annuity payment.
Solution:
∵ r = 12% p.a.
∴ i = \(\frac{r}{100}=\frac{12}{100}\) = 0.12
∵ P = ₹ 10,000
∵ A = ₹ 20,000
∵ \(\frac{1}{P}-\frac{1}{A}=\frac{i}{C}\)

∴ C = 0.12 × 20,000
∴ C = ₹ 2,400

Question 15.
For an annuity immediate paid for 3 years with interest compounded at 10% p.a. the present value is ₹ 24,000. What will be the accumulated value after 3 years? [Given (1.1)³ = 1.331]
Solution:
∵ n = 3 years
∵ P = ₹ 24,000
∵ r = 10% p.a.
∴ i = \(\frac{r}{100}=\frac{10}{100}\) = 0.1
∵ A = P(1 + i)ⁿ
∴ A = 24,000 [1 + 0.1]³
∴ A = 24,000 × (1.1)³
∴ A = 24,000 × 1.331
∴ A = ₹ 31,944

Question 16.
A person sets up a sinking fund in order to have ₹ 1,00,000 after 10 years. What amount should be deposited bi-annually in the account that pays him 5% p.a. compounded semi-annually? [Given: (1.025)²⁰ = 1.675]
Solution:
∴ A = ₹ 1,00,000
∴ n = 10 years
But, invested half yearly
∴ n = 10 × 2 = 20
∵ r = 5% p.a. compounded half yearly
∴ r = \(\frac{r}{2}=\frac{5}{2}\) = 2.5%
∴ i = \(\frac{r}{100}=\frac{2.5}{100}\) = 0.025

∴ 2,500 = C[1.675 – 1]
∴ 2,500 = C × 0.675
∴ \(\frac{2,500}{0.675}\) = C
∴ C = ₹ 3,703.70

12th Commerce Maths Digest Pdf

• 12th Commerce Maths Exercise 2.1 Solutions
• 12th Commerce Maths Exercise 2.2 Solutions
• 12th Commerce Maths Miscellaneous Exercise 2 Solutions

Insurance and Annuity Class 12 Commerce Maths 2 Chapter 2 Exercise 2.1 Answers Maharashtra Board

Balbharati Maharashtra State Board 12th Commerce Maths Digest Pdf Chapter 2 Insurance and Annuity Ex 2.1 Questions and Answers.

Std 12 Maths 2 Exercise 2.1 Solutions Commerce Maths

Question 1.
Find the premium on a property worth ₹ 25,00,000 at 3% if
(i) the property is fully insured
(ii) the property is insured for 80% of its value.
Solution:
Case-1
Property value = ₹ 25,00,000
Rate of Premium = 3%
Policy Value = ₹ 25,00,000
∴ Amount of Premium = 3% × 25,00,000 = ₹ 75,000
Case-2
Property Value = ₹ 25,00,000
Policy value = 80% × 25,00,000 = ₹ 20,00,000
Rate of Premium = 3%
∴ Amount of Premium = 3% × 20,00,000 = ₹ 60,000

Question 2.
A shop is valued at ₹ 3,60,000 for 75% of its value. If the rate of premium is 0.9%, find the premium paid by the owner of the shop. Also, find the agents commission if the agent gets commission at 15% of the premium.
Solution:
Property Value = ₹ 3,60,000
Policy Value = 75% × 3,60,000 = ₹ 2,70,000
Rate of Premium = 0.9%
∴ Amount of Premium = 0.9% × 2,70,000 = ₹ 2,430
Rate of Commission = 15%
∴ Amount of Commission = 15% × 2,430 = ₹ 364.5

Question 3.
A person insures his office valued at ₹ 5,00,000 for 80% of its value. Find the rate of premium if he pays ₹ 13,000 as premium. Also, find agent’s commission at 11%.
Solution:
Property Value = ₹ 5,00,000
Policy Value = 80% × 5,00,000 = ₹ 4,00,000
Amount of Premium = ₹ 13000
Let the rate of Premium be x%
Amount of premium = Rate × Policy Value
∴ 13000 = x% × 4,00,000
∴ \(\frac{13,000}{4,00,000}=\frac{x}{100}\)
∴ \(\frac{13,000 \times 100}{4,00,000}\) = x
∴ x = 3.25%
Rate of commission = 11%
∴ Amount of Commission = 11% × 13,000 = ₹ 1,430

Question 4.
A building is insured for 75% of its value. The annual premium at 0.70 percent amounts to ₹ 2625. If the building is damaged to the extent of 60% due to fire, how much can be claimed under the policy?
Solution:
Let the Property Value of building be ₹ x
Policy Value = 75% × x = 0.75x
Rate of Premium = 0.70%
Amount of Policy = Rate × Policy Value
2625 = 0.70% × 0.75x
\(\frac{2625}{0.75}\) = 0.70% × x
3520 = \(\frac{0.70}{100}\) × x
\(\frac{3500 \times 100}{0.70}\) = x
x = ₹ 5,00,000
∴ Damage = 60% × Property Value
= \(\frac{60}{100}\) × 5,00,000
= ₹ 3,00,000
∴ Policy Value = 0.75 × 3,00,000 = ₹ 2,25,000
∴ Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss
= \(\frac{2,25,000}{5,00,000}\) × 3,00,000
= ₹ 1,35,000

Question 5.
A stock worth ₹ 7,00,000 was insured for ₹ 4,50,000. Fire burnt stock worth ₹ 3,00,000 completely and damaged there remaining stock to the extent of 75% of its value. What amount can be claimed undertaken policy?
Solution:
Property Value = ₹ 7,00,000
Policy Value = ₹ 4,50,000
Complete Loss = 3,00,000
Partial loss = 75% × [7,00,000 – 3,00,000]
= \(\frac{75}{100}\) × 4,00,000
= ₹ 3,00,000
∴ Total loss = ₹ 3,00,000 + ₹ 3,00,000 = ₹ 6,00,000
∴ Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss
= \(\frac{4,50,000}{7,00,000}\) × 6,00,000
= ₹ 3,85,714.29

Question 6.
A cargo of rice was insured at 0.625 % to cover 80% of its value. The premium paid was ₹ 5,250. If the price of rice is ₹ 21 per kg. find the quantity of rice (in kg) in the cargo.
Solution:
Let Property Value be ₹ x
Policy Value = 80% × x = ₹ 0.8x
Rate of Policy = 0.625%
Amount of Premium = Rate × Policy value
∴ 5250 = 0.625% × 0.8x
∴ 5250 = 0.005x
∴ x = \(\frac{5250}{0.005}\)
∴ x = ₹ 10,50,000
Rate of Rice = ₹ 21/kg
∴ Quantity of Rice (in kg) = \(\frac{\text { Total value }}{\text { Rate of Rice }}\)
= \(\frac{10,50,000}{21}\)
= 50,000 kgs

Question 7.
60,000 articles costing ₹ 200 per dozen were insured against fire for ₹ 2,40,000. If 20% of the articles were burnt and 7,200 of the remaining articles were damaged to the extent of 80% of their value, find the amount that can be claimed under the policy.
Solution:
No of articles = 60,000
Cost of articles = ₹ 200/dozen
∴ Property of Value = \(\frac{60,000}{12}\) × 200 = ₹ 1o,oo,ooo
∴ Policy Value = ₹ 2,40,000
Complete Loss = 20% × 10,00,000 = ₹ 2,00,000
Partial loss = \(\frac{7200}{12}\) × 200 × 80% = ₹ 96,000
∴ Total loss = 2,00,000 + 96,000 = ₹ 2,96,000
Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss
= \(\frac{2,40,000}{10,00,000}\) × 2,96,000
= ₹ 71,040

Question 8.
The rate of premium is 2% and other expenses are 0.075%. A cargo worth ₹ 3,50,100 is to be insured so that all its value and the cost of insurance will be recovered in the event of total loss.
Solution:
Let the Policy Value of Cargo be ₹ 100 which includes insurance and other expenses
∴ Property Value = 100 – [2 + 0.075] = ₹ 97.925
If Policy Value is ₹ 100, then Property Value is ₹ 97.925
If Property Value is ₹ 3,50,100
Then policy Value = \(\frac{100 \times 3,50,100}{97.925}\) = ₹ 3,57,518.51

Question 9.
A property worth ₹ 4,00,000 is insured with three companies. A, B, and C. The amounts insured with these companies are ₹ 1,60,000, ₹ 1,00,000 and ₹ 1,40,000 respectively. Find the amount recoverable from each company in the event of a loss to the extent of ₹ 9,000.
Solution:
Property Value = ₹ 4,00,000
Loss = ₹ 9,000
Total Value of Policies = 1,60,000 + 1,00,000 + 1,40,000 = ₹ 4,00,000
Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss
Claim of company A = \(\frac{1,60,000}{40,000}\) × 9,000 = ₹ 3,600
Claim of company B = \(\frac{1,00,000}{4,00,000}\) × 9,000 = ₹ 2,250
Claim of company C = \(\frac{1,40,000}{4,00,000}\) × 9,000 = ₹ 3,150

Question 10.
A car valued at ₹ 8,00,000 is insured for ₹ 5,00,000. The rate of premium is 5% less 20%. How much will the owner bear including the premium if value of the ear is reduced to 60% of its original value.
Solution:
Property Value = ₹ 8,00,000
Policy Value = ₹ 5,00,000
Rate of Premium = 5% less 20%
= 5% – 20% × 5%
= (5 – 1)%
= 4%
Amount of Premium = 4% × 5,00,000 = ₹ 20,000
Loss = [100 – 60]% × Property Value
= 40% × 8,00,000
= ₹ 3,20,000
Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss
= \(\frac{5,00,000}{8,00,000}\) × 3,20,000
= ₹ 2,00,000
Loss bear by owner = Loss – claim + Premium
= 3,20,000 – 2,00,000 + 20,000
= ₹ 1,40,000

Question 11.
A shop and a godown worth ₹ 1,00,000 and ₹ 2,00,000 respectively were insured through an agent who was paid 12% of the total premium. If the shop was insured for 80% and the godown for 60% of their respective values, find the agent’s commission, given that the rate of premium was 0.80% less 20%.
Solution:
Rate of Premium = 0.80% Less 20%
= 0.80% – 20% × 0.80%
= (0.80 – 0.16)%
= 0.64%
For Shop
Property Value = ₹ 1,00,000
Policy Value = 80% × 1,00,000 = ₹ 80,000
Premium = 0.64% × 80,000 = ₹ 512
For Godown
Property Value = ₹ 2,00,000
Policy Value = 60% × 2,00,000 = ₹ 1,20,000
Premium = 0.64% × 1,20,000 = ₹ 768
∴ Total Premium = 512 + 768 = ₹ 1,280
Rate of Commission = 12%
∴ Agent Commission = 12% × 1,280 = ₹ 153.6

Question 12.
The rate of premium on a policy of ₹ 1,00,000 is ₹ 56 per thousand per annum. A rebate of ₹ 0.75 per thousand is permitted if the premium is paid annually. Find the net amount of premium payable if the policy holder pays the premium annually.
Solution:
Policy Value = ₹ 1,00,000
Rate of Premium = ₹ 56 per thousand p.a
Rate of Rebate = ₹ 0.75 per thousand p.a
Premium is paid annually
∴ Net rate of = 56 – 0.75 = ₹ 55.25 per thousand p.a.
∴ Net Amount ot Premium = \(\frac{1,00,000}{1000}\) × 55.25 = ₹ 5,525

Question 13.
A warehouse valued at ₹ 40,000 contains goods worth ₹ 2,40,000. The warehouse is insured against fire for ₹ 16,000 and the goods to the extent of 90% of their value. Goods worth ₹ 80,000 are completely destroyed, while the remaining goods are destroyed to 80% of their value due to a fire. The damage to the warehouse is to the extent of ₹ 8,000. Find the total amount that can be claimed.
Solution:
For Warehouse
Property Value = ₹ 40,000
Policy Value = ₹ 16,000
Loss = ₹ 8,000
Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss
= \(\frac{16,000}{40,000}\) × 8,000
= ₹ 3,200
For Goods
Property Value = ₹ 2,40,000
Policy Value = 90% × 2,40,000 = ₹ 2,16,000
Complete Loss = 80,000
Partial Loss = 80% × (2,16,000 – 80,000)
= 80% × 1,36,000
= ₹ 1,08,800
Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss
= \(\frac{2,16,000}{24,000}\) × 1,08,800
= ₹ 97,920
∴ Total Claim = 3,200 + 97,920 = ₹ 1,01,120

Question 14.
A person takes a life policy for ₹ 2,00,000 for a period of 20 years. He pays premium for 10 years during which bonus was declared at an average rate of ₹ 20 per year per thousand. Find the paid up value of the policy if he discontinuous paying premium after 10 years.
Solution:
Policy Value = ₹ 2,00,000
Rate of Bonus = ₹ 20 Per thousand p.a.
Total Bonus = \(\frac{2,00,000 \times 20}{1,000}\) = ₹ 4,000
∴ Bonus for 10 years = 4,000 × 10 = ₹ 40,000
Period of Policy = 20 years
∴ Amount of Premium = \(\frac{2,00,000}{20}\) = ₹ 10,000 p.a.
∴ Total Premium for 10 years = 10,000 × 10 = ₹ 1,00,000
∴ Paid up Value of Policy = Total premium + Total Bonus
= 1,00,000 + 40,000
= ₹ 1,40,000

12th Commerce Maths Digest Pdf

• 12th Commerce Maths Exercise 2.1 Solutions
• 12th Commerce Maths Exercise 2.2 Solutions
• 12th Commerce Maths Miscellaneous Exercise 2 Solutions

Commission, Brokerage and Discount Class 12 Commerce Maths 2 Chapter 1 Miscellaneous Exercise 1 Answers Maharashtra Board

Balbharati Maharashtra State Board 12th Commerce Maths Digest Pdf Chapter 1 Commission, Brokerage and Discount Miscellaneous Exercise 1 Questions and Answers.

Std 12 Maths 2 Miscellaneous Exercise 1 Solutions Commerce Maths

(I) Choose the correct alternative.

Question 1.
An agent who gives a guarantee to his principal that the party will pay the sale price of goods is called
(a) Auctioneer
(b) Del Credere Agent
(c) Factor
(d) Broker
Answer:
(b) Del Credere Agent

Question 2.
An agent who is given the possession of goods to be sold is known as
(a) Factor
(b) Broker
(c) Auctioneer
(d) Del Credere Agent
Answer:
(a) Factor

Question 3.
The date on which the period of the bill expires is called
(a) Legal Due Date
(b) Grace Date
(c) Nominal Due Date
(d) Date of Drawing
Answer:
(c) Nominal Due Date

Question 4.
The payment date after adding 3 days of grace period is known as
(a) The legal due date
(b) The nominal due date
(c) Days of grace
(d) Date of drawing
Answer:
(a) The legal due date

Question 5.
The sum due is also called as
(a) Face value
(b) Present value
(c) Cash value
(d) True discount
Answer:
(a) Face value

Question 6.
P is the abbreviation of
(a) Face value
(b) Present worth
(c) Cash value
(d) True discount
Answer:
(b) Present worth

Question 7.
Banker’s gain is the simple interest on
(a) Banker’s discount
(b) Face Value
(c) Cash value
(d) True discount
Answer:
(d) True discount

Question 8.
The marked price is also called as
(a) Cost price
(b) Selling price
(c) List price
(d) Invoice price
Answer:
(c) List price

Question 9.
When only one discount is given then
(a) List price = Invoice price
(b) Invoice price = Net selling price
(c) Invoice price = Cost price
(d) Cost price = Net selling price
Answer:
(b) Invoice price = Net selling price

Question 10.
The difference between the face value and present worth is called
(a) Banker’s discount
(b) True discount
(c) Banker’s gain
(d) Cash value
Answer:
(b) True discount

(II) Fill in the blanks.

Question 1.
A person who draws the bill is called ____________
Answer:
Drawee

Question 2.
An ____________ is an agent who sells the goods by auction.
Answer:
Auctioneer

Question 3.
Trade discount is allowed on the ____________ price.
Answer:
Catalogue/List

Question 4.
The banker’s discount is also called ____________.
Answer:
Commercial Discount

Question 5.
The banker’s discount is always ____________ than the true discount.
Answer:
higher

Question 6.
The diffrence between the banker’s discount and the true discount is called ____________.
Answer:
bankers gain

Question 7.
The date by which the buyer is legally allowed to pay the amount is known as ____________.
Answer:
legal due date

Question 8.
A ____________ is an agent who brings together the buyer and the seller.
Answer:
broker

Question 9.
If buyer is allowed both trade and cash discounts, ____________ discount is fist calculated on ____________ price.
Answer:
Trade, Catalogue/List

Question 10.
____________ = List price (catalogue Price) – Trade Discount.
Answer:
Invoice Price

(III) State whether each of the following is True or False.

Question 1.
A broker is an agent who gives a guarantee to the seller that the buyer will pay the sale price of goods.
Answer:
False

Question 2.
A cash discount is allowed on the list price.
Answer:
False

Question 3.
Trade discount is allowed on catalogue price.
Answer:
True

Question 4.
The buyer is legally allowed 6 days grace period.
Answer:
False

Question 5.
The date on which the period of the bill expires is called the nominal due date.
Answer:
True

Question 6.
The difference between the banker’s discount and true discount is called sum due.
Answer:
False

Question 7.
The banker’s discount is always lower than the true discount.
Answer:
False

Question 8.
The banker’s discount is also called a commercial discount.
Answer:
True

Question 9.
In general cash, the discount is more than trade discount.
Answer:
False

Question 10.
A person can get both, trade discount and a cash discount.
Answer:
True

(IV) Solve the following problems.

Question 1.
A salesman gets a commission of 6.5% on the total sales made by him and a bonus of 1% on sales over ₹ 50,000. Find his total income on a turnover of ₹ 75,000.
Solution:
Rate of commission = 6.5% on the total sales
∴ Commission on a turnover of ₹ 75,000
= \(\frac{6.5}{100}\) × 75,000
= ₹ 4,875
Rate of bonus = 1% on sales over ₹ 50,000
∴ Amount of bonus = \(\frac{1}{100}\) × (75,000 – 50,000) = ₹ 250
∴ Total income of the sales man = ₹ 4,875 + ₹ 250 = ₹ 5,125

Question 2.
A shop is sold at 30% profit, the amount of brokerage at the rate of \(\frac{3}{4}\)% amounts to ₹ 73,125. Find the cost of the shop.
Solution:
Rate of brokerage = \(\frac{3}{4}\)%
Amount of brokerage = ₹ 73,125
Let the selling price of the shop be ₹ 100 then the brokerage = ₹ \(\frac{3}{4}\)
Thus, if the amount of brokerage is ₹ \(\frac{3}{4}\) then the selling price of the shop is ₹ 100
If the amount of brokerage is ₹ 73,125, then the selling price of the shop is = 73125 × \(\frac{4}{3}\) × 100 = ₹ 97,50,000
The shop is sold at 30% profit
∴ If the cost of the shop is ₹ 100, then it is sold at ₹ 130
Thus, if the shop is sold at ₹ 130, then its cost price is ₹ 100
If the shop is sold at ₹ 97,50,000 then its cost price is = \(\frac{97,50,000 \times 100}{130}\) = ₹ 75,00,000
Then, the cost of the shop is ₹ 75,00,000

Question 3.
A merchant gives 5% commission and 1.5% delcredere to his agents. If the agent sells goods worth ₹ 30,600 how much does he get? How much does the merchant receive?
Solution:
Rate of commission = 5%
Total sales = ₹ 30,600
Amount of commission = \(\frac{5}{100}\) × 30,600
Rate of delcredere = 1.5%
= \(\frac{1.5}{100}\) × 30,600
= ₹ 459
Thus, the agents gets 1,530 + 459 = ₹ 1,989
And the merchant receives = 30,600 – 1,989 = ₹ 28,611

Question 4.
After deducting commission at 7\(\frac{1}{2}\)% on first ₹ 50,000 and 5% on the balance of sales made by him, an agent remits ₹ 93,750 to his principal. Find the value of goods sold by him.
Solution:
Rate of commission = 7\(\frac{1}{2}\)% on first ₹ 50,000
= \(\frac{7.5}{100}\) × 50,000
= ₹ 3,750
Let the total sales be ₹ x
Rate of commission on the balance sales = 5%
Commission on the balance sales = \(\frac{5}{100}\) × (x – 50000) = \(\frac{x}{20}\) – 2,500
Total commission = 3750 + \(\frac{x}{20}\) – 2,500 = \(\frac{x}{20}\) + 1,250
Now, the amount to be remitted to the principal = Value of goods sold – Commission of the agent
= x – (\(\frac{x}{20}\) + 1250)
= \(\frac{19x}{20}\) – 1250
The agents remits ₹ 93,750 to his principal
∴ \(\frac{19x}{20}\) – 1,250 = 93,750
∴ \(\frac{19x}{20}\) = 95,000
∴ x = ₹ 1,00,000
Thus, the value of the goods sold by the agent is ₹ 1,00,000

Question 5.
The present worth of ₹ 11,660 due 9 months hence is ₹ 11,000. Find the rate of interest.
Solution:
Given, PW = ₹ 11,000, SD = ₹ 11,660
n = \(\frac{9}{12}\) year = \(\frac{3}{4}\) year
We have,

∴ The rate of interest is 8% p.a.

Question 6.
An article is marked at ₹ 800, a trader allows a discount of 2.5% and gains 20% on the cost. Find the cost price of the article?
Solution:
Marked price of the article = ₹ 800
Rate of discount = 2.5%
Amount of discount = \(\frac{2.5}{100}\) × 800 = ₹ 20
∴ Selling price of the article = 800 – 20 = ₹ 780
Now, given, gain = 20%
Let cost price of the article be ₹ 100, then
The selling price of the article is ₹ 120
Thus if cost price of the articles is ₹ x
Then the selling price is ₹ 780
∴ x = \(\frac{780 \times 100}{120}\)
∴ x = 650
∴ Cost price of the article is ₹ 650

Question 7.
A salesman is paid a fixed monthly salary plus commission on the sales. If on sale of ₹ 96,000 and ₹ 1,08,000 in two successive months he receives in all ₹ 17,600 and ₹ 18,800 respectively. Find his monthly salary and rate of commission paid to him.
Solution:
Let the monthly salary of the salesman be ₹ x
And the rate of commission be y%
Income = monthly salary + commission on the sales
17600 = x + \(\frac{y}{100}\) × 96,000
∴ 17600 = x + 960y ………(1)
and 18800 = x + \(\frac{y}{100}\) × 108000
∴ 18,800 = x + 1080y ………(2)
Subtracting equation (1) from equation (2), we get
1,200 = 120y
∴ y = 10
Substituting y = 10 in (1), we get
17,600 = x + 960(10)
∴ x = 17,600 – 9,600 = 8,000
∴ Salary of the salesman = ₹ 8,000
Rate of commission = 10%

Question 8.
A merchant buys some mixers at a 15% discount on catalogue price. The catalogue price is ₹ 5,500 per price of the mixer. The freight charges amount to 2\(\frac{1}{2}\)% on the catalogue price. The merchant sells each mixer at a 5% discount on the catalogue price. His net profit is ₹ 41,250, Find the number of mixers.
Solution:
Catalogue price of a mixer = ₹ 5,500
Trade discount = 15% on catalogue price
= \(\frac{15}{100}\) × 5,500
= ₹ 825
Freight charges = 2\(\frac{1}{2}\)% of the catalogue price
= \(\frac{5}{2} \times \frac{1}{100} \times 5,500\)
= ₹ 137.5
∴ Cost price of a mixer for the merchant = 5,500 – 825 + 137.5 = 4,812,5
Catalogue price = ₹ 5,500
Rate of discount = 5%
∴ Selling price of one mixer = 5500 – \(\frac{5}{100}\) × 5,500 = ₹ 5,225
∴ Profit on one mixer = 5,225 – 4,812.5 = ₹ 412.5
Now, total profit = ₹ 41,250
∴ Number of mixers = \(\frac{41,250}{412.5}\) = 100
Thus the number of mixers is 100.

Question 9.
A bill is drawn for ₹ 7,000 on 3rd May for 3 months and is discounted on 25th May at 5.5% Find the present worth.
Solution:
Face value of the bill = ₹ 7,000
Date of drawing = 3rd May
Period = 3 months
Normal due date = 3rd August
Legal due date = 6th August
Rate of interest = 5.5%
Date of discounting = 25th May
Unexpired period (number of days from date of discounting to legal due date)

∴ Bankers discount = 7,000 × \(\frac{73}{365} \times \frac{5.5}{100}\) = ₹ 77
Also PW = SD – BD
= 7,000 – 77
= ₹ 6,923
∴ Present worth is ₹ 6,923

Question 10.
A bill was drawn on 14th April 2005 for ₹ 3,500 and was discounted on 6th July 2005 at 5% per annum. The banker paid ₹ 3,465 for the bill. Find the period of the bill.
Solution:
Face value of the bill = ₹ 3,500
Date of drawing = 14/04/2005
Date of discount = 06/07/2005
Rate of interest = 5%
Cash value = ₹ 3,465
Bankers discount = Face value – Cash value
= 3,500 – 3,465
= ₹ 35
Let the unexpired days be n days
∴ BD = \(\frac{\mathrm{FV} \times n \times r}{365 \times 100}\)
∴ 35 = \(\frac{3,500 \times n \times 5}{365 \times 100}\)
∴ n = 73 days
Thus, legal due date is 73 days from the date of discounting

∴ Legal due date = 17/09/2005
∴ Nominal due date = 14/09/2005
∴ The period of the bill is 5 months

Question 11.
The difference between true discount and banker’s discount on 6 months hence at 4% p.a. is ₹ 80. Find the true discount, banker’s discount, and amount of the bill.
Solution:
BG = BD – TD
∴ BG = ₹ 80
Also BG = \(\frac{\mathrm{TD} \times n \times r}{100}\)
∴ 80 = \(\frac{\mathrm{TD} \times 6 \times 4}{12 \times 100}\)
∴ TD = \(\frac{80 \times 100}{2}\)
∴ TD = ₹ 4,000
Now BD = TD + BG
= 4,000 + 80
= ₹ 4,080
Also, BD = \(\frac{\mathrm{FV} \times n \times r}{100}\)
∴ 4,080 = \(\frac{\mathrm{FV} \times 6 \times 4}{12 \times 100}\)
∴ FV = \(\frac{4,080 \times 100}{2}\)
∴ FV = ₹ 2,04,000
Amount of the bill = ₹ 2,04,000

Question 12.
A manufacturer makes a clear profit of 30% on the cost after allowing a 35% discount. If the cost of production rises by 20%, by what percentage should he reduce the rate of discount so as to make the same rate of profit keeping his list prices unaltered.
Solution:
Rate of discount = 35%
Let the list price be ₹ 100.
Then discount at 35% = ₹ 35
∴ Net selling price = 100 – 35 = ₹ 65 ……..(1)
The manufacturer makes a clear profit of 30% on the cost after allowing a 35% Discount.
Let the cost be ₹ 100.
Then selling price at 30% profit is 100 + 30 = ₹ 130.
Thus, if the net selling price is ₹ 130, then the cost price is ₹ 100.
But, the net selling price is ₹ 130, then the cost price is ₹ 65 ……[from (1)]
∴ The cost price is \(\frac{65}{130} \times 100\) = ₹ 50
Hence, we have,

Now, the cost of production has increased by 20%.
Let the old cost price be ₹ 100.
∴ The new cost price is ₹ 120.
But, the old cost price is ₹ 50.
∴ The new cost price is = \(\frac{50}{100} \times 120\) = ₹ 60.
The old net price is ₹ 65.
Now 20% of ₹ 65 = \(\frac{20}{100} \times 65\) = ₹ 13
∴ New net price = 65 + 13 = ₹ 78
Hence, we have

Now, 100 – 78 = ₹ 22
Thus, the rate of discount should be reduced by 22%, The original rate of discount is 35%.
Hence, the reduction in discount should be (35 – 22)% = 13%
so as to make the same rate of profit, keeping the list price unaltered.

Question 13.
A trader offers a 25% discount on the catalogue price of the radio and yet makes a 20% profit. If he gains ₹ 160 per radio, what must be the catalogue price of the radio?
Solution:
Rate of discount = 25% on the catalogue price of a radio.
Let the catalogue price of the radio be ₹ 100.
Then, the discount on a radio = ₹ 25.
Net selling price = 100 – 25 = ₹ 75.
He makes a profit of 20%.
Let the cost price be ₹ 100.
Then, at 20% profit, net selling price = ₹ 120.
Thus, if net SP is ₹ 120, then cost price is ₹ 100.
But, the net SP is ₹ 75.
∴ The cost price is \(\frac{75}{120}\) × 100 = \(\frac{750}{12}\) = ₹ 62.50
∴ Profit on a radio set = 75 – 62.5 = ₹ 12.50
Thus, if the profit on a radio set is ₹ 12.50 then its catalogue price is ₹ 100.
But the profit on a radio set is ₹ 160.
∴ The catalogue price of radio = \(\frac{160}{12.50}\) × 100
= 12.80 × 100
= ₹ 1,280
∴ Thus, the catalogue price of the radio is ₹ 1280

Question 14.
A bill of ₹ 4,800 was drawn on 9th March 2006 at 6 months and was discounted on 19th April 2006 for 6\(\frac{1}{4}\)% p.a. How much does the banker charge and how much does the holder receive?
Solution:
Face value of the bill = ₹ 4.800
Date of drawing = 09/03/2006
Period of the bill = 6 months
Normal due date = 09/09/2006
Legal due date = 12/09/2006
Rate of discount = 6\(\frac{1}{4}\)% = 6.25%
Now, for the unexpired

Thus the banker charges ₹ 120
Amount received by the holder = 4,800 – 120 = ₹ 4,680

Question 15.
A bill of ₹ 65,700 drawn on July 10 for 6 months was discounted for ₹ 65,160 at 5% p.a. On what day was the bill discounted?
Solution:
BD = FV – Cash value
= 65,700 – 65,160
= ₹ 540
Let the unexpired days be x days
BD = \(\frac{\mathrm{FV} \times n \times r}{100}\)
∴ 540 = \(\frac{65,700 \times x \times 5}{365 \times 100}\)
∴ x = 60 days
The unexpired days = 60 days
Date-of drawing = 10th July
Period of the bill = 6 months
Nominal due date = 10th January (next year)
Legal due date = 13th January (next year)
Then the date of discount is 60 days before, the legal due date

∴ The date of discounting is 14th November

Question 16.
An agent sold a car and charged a 3% commission on the sale value. If the owner of the car received ₹ 48,500, find the sale value of the car. If the agent charged 2% from the buyer, find his total remuneration.
Solution:
Let the sale value of the car be ₹ x
Rate of commission of the agent = 3%
Since the owner received ₹ 48,500 after agent has charged his commission
x – \(\frac{3 x}{100}\) = 48500
∴ \(\frac{97 x}{100}\) = 48500
∴ x = \(\frac{48,500 \times 100}{97}\)
∴ x = ₹ 50,000
∴ Sale value of the car = ₹ 50,000
Against commission received from the owner = \(\frac{3}{100}\) × 50,000 = ₹ 1500
Against commission received from the buyer = \(\frac{2}{100}\) × 50,000 = ₹ 1000
∴ Agents total remuneration = 1,500 + 1,000 = ₹ 2,500

Question 17.
An agent is paid a commission of 4% on cash sales and 6% on credit sales made by him. If on the sale of ₹ 51,000 the agent claims a total commission of ₹ 2,700, find the sales made by him for cash and on credit.
Solution:
Total sales = ₹ 51,000
Let eash sales be ₹ x
∴ Credit sales = ₹ (51,000 – x)
Agent’s commission on cash sales = 4%
= \(\frac{4}{100}\) × x
= \(\frac{4x}{100}\)
Commission on credit sales = 6%
= \(\frac{6}{100}\)(51,000 – x)
Given total commission = ₹ 2,700

∴ Cash sales = ₹ 18,000
∴ Credit sales = 51,000 – 18,000 = ₹ 33,000

12th Commerce Maths Digest Pdf

• 12th Commerce Maths Exercise 1.1 Solutions
• 12th Commerce Maths Exercise 1.2 Solutions
• 12th Commerce Maths Miscellaneous Exercise 1 Solutions

Commission, Brokerage and Discount Class 12 Commerce Maths 2 Chapter 1 Exercise 1.2 Answers Maharashtra Board

Balbharati Maharashtra State Board 12th Commerce Maths Digest Pdf Chapter 1 Commission, Brokerage and Discount Ex 1.2 Questions and Answers.

Std 12 Maths 2 Exercise 1.2 Solutions Commerce Maths

Question 1.
What is the present worth of a sum of ₹ 10,920 due six months hence at 8% p.a simple interest?
Solution:
Given, SD = ₹ 10,920
n = \(\frac{6}{12}\) year = \(\frac{1}{2}\) year
r = 8%
We have,

Thus the present worth is ₹ 10,500

Question 2.
What is the sum due of ₹ 8,000 due 4 months at 12.5% simple interest?
Solution:
Given, PW = ₹ 8,000, n = \(\frac{4}{12}\) year = \(\frac{1}{3}\) year, r = 12.5%
We have,

Thus, the sum due is ₹ 8,333.33

Question 3.
The true discount on the sum due 8 months hence at 12% p.a. is ₹ 560. Find the sum due and present worth of the bill.
Solution:
Given, TD = ₹ 560, n = \(\frac{8}{12}\) year = \(\frac{2}{3}\) year, r = 12%
We have,
TD = \(\frac{\mathrm{PW} \times n \times r}{100}\)
∴ 560 = \(\frac{\mathrm{PW} \times 2 \times 12}{3 \times 100}\)
∴ PW = 560 × \(\frac{25}{2}\) = ₹ 7,000
Now, SD = PW + TD
= 7,000 + 560
= ₹ 7,560

Question 4.
The true discount on a sum is \(\frac{3}{8}\) of the sum due at 12% p.a. Find the period of the bill.
Solution:

8 × n × 12 = 3(100 + n × 12)
96n = 300 + 36n
60n = 300
∴ n = 5
∴ Period of the bill = 5 years.

Question 5.
20 copies of a book can be purchased for a certain sum payable at the end of 6 months and 21 copies for the same sum in ready cash. Find the rate of interest.
Solution:
Given, n = \(\frac{6}{12}\) year = \(\frac{1}{2}\) year
Let the sum payable be ₹ x
Let the rate of interest be r%
According to given condition,
PW of one book = \(\frac{x}{21}\)
SD of one book = \(\frac{x}{20}\)

Thus, the rate of interest is 10%.

Question 6.
Find the true discount, Banker’s discount, and Banker’s gain on a bill of ₹ 4,240 due 6 months hence at 9% p.a.
Solution:

And, Banker’s Gain (BG) = BD – TD
= 190.80 – 182.58
= ₹ 8.22

Question 7.
The true discount on a bill is ₹ 2,200 and bankers discount is ₹ 2,310. If the bill is due 10 months, hence, find the rate of interest.
Solution:
Given, TD = ₹ 2,200, BD = ₹ 2,310
n = \(\frac{10}{12}=\frac{5}{6}\) year

∴ \(\frac{r}{120}=\frac{1}{20}\)
∴ r = 6%
Thus, rate of interest is 6%

Question 8.
A bill of ₹ 6,395 drawn on 19th January 2015 for 8 months was discounted on 28th February 2015 at 8% p.a. interest. What is the banker’s discount? What is the cash value of the bill?
Solution:
Face value = ₹ 6,395
Date of drawing = 19/01/2015
Period of the bill = 8 months
Nominal Due date = 19/09/2015
Legal due date = 22/09/2015
Date of discounting = 28/02/2015
Now, the unexpired period = Legal due date – Date of discounting
= 22/09/2015 – 28/02/2015
= days (as shown below)

Cash Value = FV – BD
= 6,395 – 313.12
= ₹ 6,621.38

Question 9.
A bill of ₹ 8,000 drawn on 5th January 1998 for 8 months was discounted for ₹ 7,680 on a certain date. Find the date on which it was discounted at 10% p.a.
Solution:
Bankers discount (BD) = FV – cash value
= 8,000 – 7,680
= ₹ 320
Let the unexpired period be x days
∴ BD = \(\frac{\mathrm{FV} \times x \times r}{365 \times 100}\)
∴ 320 = \(\frac{8,000 \times x \times 10}{365 \times 100}\)
∴ x = 146 days
∴ The unexpired days = 146 days
Date of drawing = 05/01/1998
Period of bill = 8 months
Nominal due date = 05/09/1998
Legal due date = 08/09/1998
Thus, the date of discounting is 146 days before the legal due date

∴ Date of discounting of the bill is 15th April 1998

Question 10.
A bill drawn on 5th June for 6 months was discounted at the rate of 5% p.a. on 19th October. If the cash value of the bill is ₹ 43,500, find the face value of the bill.
Solution:
Date of drawing = 5th June
Period of bill = 6 months
Nominal due date = 5th December
Legal due date = 8th December
Date of discounting = 19th October
Rate of interest = 5% p.a.
Let the face value of the bill be ₹ x
The unexpired period

Question 11.
A bill was drawn on 14th April for ₹ 7,000 and was discounted on 6th July at 5% p.a. The Banker paid ₹ 6,930 for the bill. Find the period of the bill.
Solution:
Face value = ₹ 7,000, cash value = ₹ 6,930
∴ Banker’s discount = 7,000 – 6,930 = ₹ 70
Date of drawing = 14/04
Date of discounting = 06/07
Rate of interest = 5%
Let the unexpired period = x days
∴ BD = \(\frac{7,000 \times x \times 5}{365 \times 100}\)
∴ 70 = \(\frac{70 \times x}{73}\)
∴ x = 73 days
∴ Legal due date of the bill is 73 days after the date of discounting.

∴ Legal due date = 17/09
∴ Nominal due date = 14/09
∴ Period of the bill = 5 months

Question 12.
If the difference between true discount and banker’s discount on a sum due 4 months hence is ₹ 20. Find true discount, banker’s discount and amount of bill, the rate of simple interest charged is 5% p.a.
Solution:
Banker’s gain (BG) = Banker’s discount (BD) – True Discount (TD)
∴ BG = ₹ 20
Also, BG = \(\frac{\mathrm{TD} \times n \times r}{100}\)
∴ 20 = \(\frac{\mathrm{TD} \times 4 \times 5}{12 \times 100}\)
∴ 20 = \(\frac{\mathrm{TD}}{60}\)
∴ TD = ₹ 1200
Now, BD = BG + TD
= 20 + 1,200
= ₹ 1,220
Also, BD = \(\frac{\mathrm{FV} \times n \times r}{100}\)
∴ 1,220 = \(\frac{\mathrm{FV} \times 4 \times 5}{12 \times 100}\)
∴ FV = 1,200 × 60 = ₹ 73,200
∴ Amounting the bill = ₹ 73,200

Question 13.
A bill of ₹ 51,000 was drawn on 18th February 2010 for 9 months. It was encashed on 28th June 2010 at 5% p.a. Calculate the banker’s gain and true discount.
Solution:
Face Value = ₹ 51,000
Date of drawing = 18/02/2010
Period of the bill = 9 months
Nominal due date = 18/11/2010
Legal due date = 21/11/2010
Date of discounting = 28/06/2010
Unexpired period

∴ TD = ₹ 1,000
∴ BG = BD – TD
= 1,020 – 1,000
= ₹ 20

Question 14.
A certain sum due 3 months hence is \(\frac{21}{20}\) of the present worth, what is the rate of interest.
Solution:

Question 15.
A bill of a certain sum drawn on 28th February 2007 for 8 months was encashed on 26th March 2007 for ₹ 10,992 at 14% p.a. Find the face value of the bill.
Solution:
Date drawing = 28/02/2007
Period of the bill = 8 months
Nominal due date = 28/10/2007
Legal due date = 31/10/2007
Date of discounting = 26/03/2007
Cash value = ₹ 10,992
Rate of interest = 14%
Let face value of the bill = ₹ x
Bankers discount = Face value – Cash value = x – 10,992
Also, Banker s discount = \(\frac{F V \times n \times r}{365 \times 100}\)
Where n is the unexpired days

Thus face value of the bill = ₹ 12,000

12th Commerce Maths Digest Pdf

• 12th Commerce Maths Exercise 1.1 Solutions
• 12th Commerce Maths Exercise 1.2 Solutions
• 12th Commerce Maths Miscellaneous Exercise 1 Solutions

Commission, Brokerage and Discount Class 12 Commerce Maths 2 Chapter 1 Exercise 1.1 Answers Maharashtra Board

Balbharati Maharashtra State Board 12th Commerce Maths Digest Pdf Chapter 1 Commission, Brokerage and Discount Ex 1.1 Questions and Answers.

Std 12 Maths 2 Exercise 1.1 Solutions Commerce Maths

Question 1.
An agent charges a 12% commission on the sales. What does he earn if the total sale amounts to ₹ 48,000? What does the seller get?
Solution:
Rate of commission = 12%
Total sales = ₹ 48,000
Agent’s commission = \(\frac {12}{100}\) × 48,000
= ₹ 5,760
Amount received by the seller = Total sales – commission
= ₹ 8,000 – ₹ 5760
= ₹ 2,240

Question 2.
A salesman receives a 3% commission on sales up to ₹ 50,000 and a 4% commission on sales over ₹ 50,000. Find his total income on the sale of ₹ 2,00,000.
Solution:
Total sales = ₹ 2,00,000
Rate of commission upto ₹ 50,000 = 3%
= \(\frac{3}{100}\) × 50,000
= ₹ 1,500
Rate of commission on the sales over ₹ 50,000 = 4%
Sales over ₹ 50,000 is 2,00,000 – 50,000 = ₹ 1,50,000
Commission on sales over ₹ 50,000 = \(\frac{4}{100}\) × 1,50,000 = ₹ 6,000
His total income = ₹ 1,500 + ₹ 6,000 = ₹ 7,500

Question 3.
Ms. Saraswati was paid ₹ 88,000 as commission on the sale of computers at the rate of 12.5%. If the price of each computer was ₹ 32,000, how many computers did she sell?
Solution:
Total commission = ₹ 88,000
Rate of commission = 12.5%
Let the number of computers sold be x
since price of each computer = ₹ 32,000
Total sales = ₹ 32,000x
Total commission = 12.5% of total sales
88,000 = \(\frac{12.5}{100}\) × 32,000x
= \(\frac{125}{1000}\) × 32,000x
x = \(\frac{88,000}{125 \times 32}\)
x = 22

Question 4.
Anita is allowed 6.5% commission on the total sales made by her, plus, a bonus of \(\frac{1}{2}\)% on the sale over ₹ 20,000. If her total commission amounts to ₹ 3,400. Find the sales made by her.
Solution:
Let the total sales made by Anita be ₹ x
Rate of commission = 6.5% of total sales
= \(\frac{6.5}{100} \times x\)
= \(\frac{65 x}{1,000}\)
= \(\frac{13 x}{200}\)

Question 5.
Priya gets a salary of ₹ 15,000 per month and a commission of 8% on sales over ₹ 50,000. If she gets ₹ 17,400 in a certain month. Find the sales made by her in that month.
Solution:
Let the total sales made by Priya be ₹ x
Salary of Priya = ₹ 15,000
Commission = Total earning – salary
= ₹ 17,400 – ₹ 15,000
= ₹ 2,400
Commission = 8% on the sales over ₹ 50,000
2400 = \(\frac{8}{100}\) (x – 50000)
\(\frac{2,400 \times 100}{8}\) = x – 50,000
30,000 = x – 50,000
30,000 + 50,000 = x
∴ x = ₹ 80,000

Question 6.
The income of the broker remains unchanged though the rate of commission is increased from 4% to 5%. Find the percentage reduction in the value of the business.
Solution:
Let the original value of business be ₹ 100
Original rate of commission = 4%
∴ Original commission = \(\frac{4}{100}\) × 100 = ₹ 4
Let the new value of business be ₹ x
The new rate of commission = 5%
∴ New commission = \(\frac{5}{100}\) × x = \(\frac{x}{20}\)
Given, original income = New income
4 = \(\frac{x}{20}\)
∴ x = ₹ 80
Thus there is 20% reduction in the value of the business.

Question 7.
Mr. Pavan is paid a fixed weekly salary plus commission based on a percentage of sales made by him. If on the sale of ₹ 68,000 and ₹ 73,000 in two successive weeks, he received in all ₹ 9,880 and ₹ 10,180. Find his weekly salary and the rate of commission paid to him.
Solution:
Let the weekly salary of Mr. Pavan be ₹ x and the rate of commission paid to him be y%
Income = Weekly salary + Commission on the sales
∴ 9,880 = x + \(\frac{y}{100}\) × 68,000
i.e. 9,880 = x + 680y …….(1)
Also, 10,180 = x + \(\frac{y}{100}\) × 73,000
i.e 10,180 = x + 730y ………(2)
Subtracting (1) from (2), we get
50y = 300
∴ y = 6
Substituting y = 6 in equation (1)
9,880 = x + 680(6) ‘
∴ 9,880 – 4,080 = x
∴ x = 5,800
Weekly salary = ₹ 5,800
Rate of commission = 6%

Question 8.
Deepak’s salary was increased from ₹ 4,000 to ₹ 5,000. The sales being the same, due to a reduction in the rate of commission from 3% to 2%, his income remained unchanged. Find his sales.
Solution:
Let Deepak’s total sales be ₹ x
Original salary of Deepak = ₹ 4,000
Original rate of commission = 3%
His new salary = ₹ 5,000
New rate of commission = 2%
Original income = New income (given)
4000 + \(\frac{3 x}{100}\) = 5000 + \(\frac{2 x}{100}\)
\(\frac{3 x}{100}-\frac{2 x}{100}\) = 5,000 – 4,000
\(\frac{x}{100}\) = 1000
x = ₹ 1,00,000
∴ His total sales = ₹ 1,00,000

Question 9.
An agent is paid a commission of 7% on cash sales and 5% on credit sales made by him. If on the sale of ₹ 1,02,000 the agent claims a total commission of ₹ 6,420, find his cash sales and credit sales.
Solution:
Total Sales = ₹ 1,02,000
Let cash sales ₹ x
∴ Credit sales = ₹ (1,02,000 – x)
Agent’s commission on cash sales = 7%
= \(\frac{7}{100}\) × x
= \(\frac{7x}{100}\)
Commission on credit sales = 5%
= \(\frac{5}{100}\)(1,02,000 – x)
Given, Total commission = ₹ 6,420
∴ \(\frac{7x}{100}\) + \(\frac{5}{100}\)(1,02,000 – x) = 6420
∴ \(\frac{7x}{100}\) + 5100 – \(\frac{5x}{100}\) = 6,420
∴ \(\frac{2x}{100}\) = 6,420 – 5,100
∴ \(\frac{2x}{100}\) = 1320
∴ x = ₹ 66,000
∴ Cash sales = ₹ 66,000
∴ Credit sales = 1,02000 – 66,000 = ₹ 36,000

Question 10.
Three cars were sold through an agent for ₹ 2,40,000, ₹ 2,22,000 and ₹ 2,25,000 respectively. The rates of the commission were 17.5% on the first, 12.5% on the second. If the agent overall received 14% commission on the total sales, find the rate of commission paid on the third car.
Solution:
Total selling price of three cars = 2,40,000 + 2,22,000 + 2,25,000 = ₹ 6,87,000
Commission on total sales = 14%
= \(\frac{14}{100}\) × 6,87,000
= ₹ 96,180
Selling price of first car = ₹ 2,40,000
Rate of commission = 17.5% = \(\frac{17.5}{100}\) × 2,40,000
∴ Commission on first car = ₹ 42,000
Selling price of second car = ₹ 2,22,000
Rate of commission = 12.5% = \(\frac{12.5}{100}\) × 2,22,000
∴ Commission on second car = ₹ 27,750
Selling price of third car = ₹ 2,25,000
Let the rate of commission be x%
Commission on third car = \(\frac{x}{100}\) × 2,25,000
96,180 – (42,000 + 27,750) = \(\frac{x}{100}\) × 2,25,000
\(\frac{26,430 \times 100}{2,25,000}\) = x
∴ x = 11.75
∴ Rate of commission on the third car = 11.75%

Question 11.
Swatantra Distributors allows a 15% discount on the list price of the washing machines. Further 5% discount is giver for cash payment. Find the list price of the washing machine if it was sold for the net amount of ₹ 38,356.25.
Solution:
Let the list price of the washing machine be ₹ 100
Trade discount = 15% = \(\frac{15}{100}\) × 100 = ₹ 15
∴ Invoice price =100 – 15 = ₹ 85
Cash discount = 5% = \(\frac{5}{100}\) × 85 = ₹ 4.25
∴ Net price = 85 – 4.25 = ₹ 80.75
Thus if List price is 100 than Net price is 80.75
if List price is x than Net price is 38,356.25.
∴ x = \(\frac{38356.25 \times 100}{80.75}\)
∴ x = ₹ 47,500
The list price of the washing machine is ₹ 47,500

Question 12.
A bookseller received ₹ 1,530 as a 15% commission on the list price. Find the list price of the books.
Solution:
Let the list price of the books be ₹ x
Rate of commission = 15%
Book seller’s commission = ₹ 1,530
∴ \(\frac{15}{100}\) × x = 1,530
∴ x = \(\frac{1,530 \times 100}{15}\)
∴ x = ₹ 10,200

Question 13.
A retailer sold a suit for ₹ 8,832 after allowing an 8% discount on market price and a further 4% cash discount. If he made 38% profit, find the cost price and the market price of the suit.
Solution:
Let the marked price of the suit be ₹ 100
Trade discount = 8% = \(\frac{8}{100}\) × 100 = ₹ 8
Invoice price = 100 – 8 = ₹ 92
Cash discount = 4% = \(\frac{4}{100}\) × 92 = ₹ 3.68
∴ Net price = 92 – 3.68 = ₹ 88.32
Thus if list price is 100 then net price is 88.32, if list price is x then net price is 8,832
∴ x = \(\frac{8,832 \times 100}{88.32}\)
∴ x = ₹ 10,000
The retailer made 38% profit.
Let the CP of the suit be ₹ 100
∴ SP of the suit = 100 + 38 = ₹ 138
Thus if the SP of the suit is ₹ 138 then its CP is ₹ 100
If the SP of the suit is 88.32 then its
CP = \(\frac{88.32 \times 100}{138}\) = ₹ 6400

Question 14.
An agent charges 10% commission plus 2% delcredere. If he sells goods worth ₹ 37,200, find his total earnings.
Solution:
Total sales = ₹ 37,200
Rate of commission = 10%
Agents commission = \(\frac{4}{100}\) × 37200 = ₹ 3720
Rate of delcredere = 2%
Amount of delcredere = \(\frac{2}{100}\) × 37,200 = ₹ 744
Total earning of the agent = ₹ 3,720 + ₹ 744 = ₹ 4,464

Question 15.
A whole seller allows a 25% trade discount and 5% cash discount. What will be the net price of an article marked at ₹ 1600?
Solution:
Marked price of the article = ₹ 1,600
Trade discount = 25%
= \(\frac{25}{100}\) × 1,600
= ₹ 400
∴ Invoice price = 1,600 – 400 = ₹ 1,200
Cash discount = 5%
= \(\frac{5}{100}\) × 1,200
= ₹ 60
∴ Net price = 1,200 – 60 = ₹ 1,140

12th Commerce Maths Digest Pdf

• 12th Commerce Maths Exercise 1.1 Solutions
• 12th Commerce Maths Exercise 1.2 Solutions
• 12th Commerce Maths Miscellaneous Exercise 1 Solutions

Probability Distributions Class 12 Commerce Maths 2 Chapter 8 Miscellaneous Exercise 8 Answers Maharashtra Board

Balbharati Maharashtra State Board 12th Commerce Maths Solution Book Pdf Chapter 8 Probability Distributions Miscellaneous Exercise 8 Questions and Answers.

Std 12 Maths 2 Miscellaneous Exercise 8 Solutions Commerce Maths

(I) Choose the correct alternative.

Question 1.
F(x) is c.d.f. of discreter r.v. X whose p.m.f. is given by P(x) = \(k\left(\begin{array}{l}
4 \\
x
\end{array}\right)\), for x = 0, 1, 2, 3, 4 & P(x) = 0 otherwise then F(5) = __________
(a) \(\frac{1}{16}\)
(b) \(\frac{1}{8}\)
(c) \(\frac{1}{4}\)
(d) 1
Answer:
(d) 1

Question 2.
F(x) is c.d.f. of discrete r.v. X whose distribution is

then F(-3) = __________
(a) 0
(b) 1
(c) 0.2
(d) 0.15
Answer:
(a) 0

Question 3.
X : number obtained on uppermost face when a fair die is thrown then E(X) = __________
(a) 3.0
(b) 3.5
(c) 4.0
(d) 4.5
Answer:
(b) 3.5

Question 4.
If p.m.f. of r.v. X is given below.

then Var(X) = __________
(a) p²
(b) q²
(c) pq
(d) 2pq
Answer:
(d) 2pq

Question 5.
The expected value of the sum of two numbers obtained when two fair dice are rolled is __________
(a) 5
(b) 6
(c) 7
(d) 8
Answer:
(c) 7

Question 6.
Given p.d.f. of a continuous r.v. X as
f(x) = \(\frac{x^{2}}{3}\) for -1 < x < 2
= 0 otherwise then F(1) =
(a) \(\frac{1}{9}\)
(b) \(\frac{2}{9}\)
(c) \(\frac{3}{9}\)
(d) \(\frac{4}{9}\)
Answer:
(b) \(\frac{2}{9}\)

Question 7.
X is r.v. with p.d.f.
f(x) = \(\frac{k}{\sqrt{x}}\), 0 < x < 4
= 0 otherwise then E(X) = __________
(a) \(\frac{1}{3}\)
(b) \(\frac{4}{3}\)
(c) \(\frac{2}{3}\)
(d) 1
Answer:
(b) \(\frac{4}{3}\)

Question 8.
If X follows B(20, \(\frac{1}{10}\)) then E(X) = __________
(a) 2
(b) 5
(c) 4
(d) 3
Answer:
(a) 2

Question 9.
If E(X) = m and Var(X) = m then X follows __________
(a) Binomial distribution
(b) Possion distribution
(c) Normal distribution
(d) none of the above
Answer:
(b) Possion distribution

Question 10.
If E(X) > Var(X) then X follows __________
(a) Binomial distribution
(b) Possion distribution
(c) Normal distribution
(d) none of the above
Answer:
(a) Binomial distribution

(II) Fill in the blanks.

Question 1.
The values of discrete r.v. are generally obtained by __________
Answer:
counting

Question 2.
The values of continuous r.v. are generally obtained by __________
Answer:
measurement

Question 3.
If X is dicrete random variable takes the values x₁, x₂, x₃, …… x_n then \(\sum_{i=1}^{n} p\left(x_{i}\right)\) = __________
Answer:
1

Question 4.
If f(x) is distribution function of discrete r.v. X with p.m.f. p(x) = \(\frac{x-1}{3}\) for x = 1, 2, 3, and p(x) = 0 otherwise then F(4) = __________
Answer:
1

Question 5.
If f(x) is distribution function of discrete r.v. X with p.m.f. p(x) = \(k\left(\begin{array}{l}
4 \\
x
\end{array}\right)\) for x = 0, 1, 2, 3, 4, and p(x) = 0 otherwise then F(-1) = __________
Answer:
0

Question 6.
E(X) is considered to be __________ of the probability distribution of X.
Answer:
centre of gravity

Question 7.
If X is continuous r.v. and f(x_i) = P(X ≤ x_i) = \(\int_{-\infty}^{x_{i}} f(x) d x\) then f(x) is called __________
Answer:
Cumulative Distribution Function

Question 8.
In Binomial distribution probability of success ________ from trial to trial.
Answer:
remains constant/independent

Question 9.
In Binomial distribution, if n is very large and probability success of p is very small such that np = m (constant) then ________ distribution is applied.
Answer:
Possion

(III) State whether each of the following is True or False.

Question 1.
If P(X = x) = \(k\left(\begin{array}{l}
4 \\
x
\end{array}\right)\) for x = 0, 1, 2, 3, 4, then F(5) = \(\frac{1}{4}\) when f(x) is c.d.f.
Answer:
False

Question 2.

If F(x) is c.d.f. of discrete r.v. X then F(-3) = 0.
Answer:
True

Question 3.
X is the number obtained on the uppermost face when a die is thrown the E(X) = 3.5.
Answer:
True

Question 4.
If p.m.f. of discrete r.v.X is

then E(X) = 2p.
Answer:
True

Question 5.
The p.m.f. of a r.v. X is p(x) = \(\frac{2 x}{n(n+1)}\), x = 1, 2,……n
= 0 otherwise,
Then E(X) = \(\frac{2 n+1}{3}\)
Answer:
True

Question 6.
If f(x) = kx (1 – x) for 0 < x < 1
= 0 otherwise then k = 12
Answer:
False

Question 7.
If X ~ B(n, p) and n = 6 and P(X = 4) = P(X = 2) then p = \(\frac{1}{2}\).
Answer:
True

Question 8.
If r.v. X assumes values 1, 2, 3,………, n with equal probabilities then E(X) = \(\frac{(n+1)}{2}\)
Answer:
True

Question 9.
If r.v. X assumes the values 1, 2, 3,………, 9 with equal probabilities, E(X) = 5.
Answer:
True

(IV) Solve the following problems.

Part – I

Question 1.
Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.
(i) An economist is interested in knowing the number of unemployed graduates in the town with a population of 1 lakh.
Solution:
X = No. of unemployed graduates in a town.
∵ The population of the town is 1 lakh
∴ X takes finite values
∴ X is a Discrete Random Variable
∴ Range of = {0, 1, 2, 4, …. 1,00,000}

(ii) Amount of syrup prescribed by a physician.
Solution:
X : Amount of syrup prescribed.
∴ X Takes infinite values
∴ X is a Continuous Random Variable.

(iii) A person on a high protein diet is interested in the weight gained in a week.
Solution:
X : Gain in weight in a week.
X takes infinite values
∴ X is a Continuous Random Variable.

(iv) Twelve of 20 white rats available for an experiment are male. A scientist randomly selects 5 rats and counts the number of female rats among them.
Solution:
X : No. of female rats selected
X takes finite values.
∴ X is a Discrete Random Variable.
Range of X = {0, 1, 2, 3, 4, 5}

(v) A highway safety group is interested in the speed (km/hrs) of a car at a checkpoint.
Solution:
X : Speed of car in km/hr
X takes infinite values
∴ X is a Continuous Random Variable.

Question 2.
The probability distribution of a discrete r.v. X is as follows.

(i) Determine the value of k.
(ii) Find P(X ≤ 4), P(2 < X < 4), P(X ≥ 3).
Solution:
(i) Assuming that the given distribution is a p.m.f. of X
∴ Each P(X = x) ≥ 0 for x = 1, 2, 3, 4, 5, 6
k ≥ 0
ΣP(X = x) = 1 and
k + 2k + 3k + 4k + 5k + 6k = 1
∴ 21k = 1 ∴ k = \(\frac{1}{21}\)

(ii) P(X ≤ 4) = 1 – P(X > 4)
= 1 – [P(X = 5) + P(X = 6)]
= 1 – [latex]\frac{5}{21}+\frac{6}{21}[/latex]
= 1 – \(\frac{11}{21}\)
= \(\frac{10}{21}\)
P(2 < X < 6) = p(3) + p(4) + p(5)
= 3k + 4k + 5k
= \(\frac{3}{21}+\frac{4}{21}+\frac{5}{21}\)
= \(\frac{12}{21}\)
= \(\frac{4}{7}\)

(iii) P(X ≥ 3) = p(3) + p(4) + p(5) + p(6)
= 3k + 4k + 5k + 6k

Question 3.
Following is the probability distribution of an r.v. X.

Find the probability that
(i) X is positive.
(ii) X is non-negative.
(iii) X is odd.
(iv) X is even.
Solution:
(i) P(X is positive)
P(X = 0) = p(1) + p(2) + p(3)
= 0.25 + 0.15 + 0.10
= 0.50

(ii) P(X is non-negative)
P(X ≥ 0) = p(0) + p(1) + p(2) + p(3)
= 0.20 + 0.25 + 0.15 + 0.10
= 0.70

(iii) P(X is odd)
P(X = -3, -1, 1, 3)
= p(- 3) +p(-1) + p(1) + p(3)
= 0.05 + 0.15 + 0.25 + 0.10
= 0.55

(iv) P(X is even)
= 1 – P(X is odd)
= 1 – 0.55
= 0.45

Question 4.
The p.m.f of a r.v. X is given by
\(P(X=x)= \begin{cases}\left(\begin{array}{l}
5 \\
x
\end{array}\right) \frac{1}{2^{5}}, & x=0,1,2,3,4,5 . \\
0 & \text { otherwise }\end{cases}\)
Show that P(X ≤ 2) = P(X ≥ 3).
Solution:
For x = 0, 1, 2, 3, 4, 5

Question 5.
In the following probability distribution of an r.v. X

Find a and obtain the c.d.f. of X.
Solution:
Given distribution is p.m.f. of r.v. X
ΣP(X = x) = 1
∴ p(1) + p(2) + p(3) + p(4) + p(5) = 1

Question 6.
A fair coin is tossed 4 times. Let X denote the number of heads obtained. Identify the probability distribution of X and state the formula for p.m.f. of X.
Solution:
A fair coin is tossed 4 times
∴ Sample space contains 16 outcomes
Let X = Number of heads obtained
∴ X takes the values x = 0, 1, 2, 3, 4.
∴ The number of heads obtained in a toss is an even

Question 7.
Find the probability of the number of successes in two tosses of a die, where success is defined as (i) number greater than 4 (ii) six appearing in at least one toss.
Solution:
S : A die is tossed two times
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
n(S) = 36
(i) X : No. is greater than 4
Range of X = {0, 1, 2}

(ii) X : Six appears on aleast one die.
Range of X = {0, 1, 2}

Question 8.
A random variable X has the following probability distribution.

Determine (i) k, (ii) P(X < 3), (iii) P(X > 6), (iv) P(0 < X < 3).
Solution:
(i) It is a p.m.f. of r.v. X
Σp(x) = 1
p(1) + p(2) + p(3) + p(4) + p(5) + p(6) + p(7) = 1
k + 2k + 2k + 3k + k² + 2k² + 7k² + k = 1
9k + 10k² = 1
10k² + 9k – 1 = 0
10k² +10k – k – 1 = 0
∴ 10k(k + 1) – 1(k + 1) = 0
∴ (10k – 1) (k + 1) = 0
∴ 10k – 1 = 0r k + 1 = 0
∴ k = \(\frac{1}{10}\) or k = -1
k = -1 is not accepted, p(x) ≥ 0, ∀ x ∈ R
∴ k = \(\frac{1}{10}\)

(ii) P(X < 3) = p(1) + p(2)
= k + 2k
= 3k
= 3 × \(\frac{1}{10}\)
= \(\frac{3}{10}\)

(iii) P(X > 6) = p(7)
= 7k² + k
= \(7\left(\frac{1}{10}\right)^{2}+\frac{1}{10}\)
= \(\frac{7}{100}+\frac{1}{10}\)
= \(\frac{17}{100}\)

(iv) P(0 < X < 3) = p(1) + p(2)
= k + 2k
= 3k
= 3 × \(\frac{1}{10}\)
= \(\frac{3}{10}\)

Question 9.
The following is the c.d.f. of a r.v. X.

Find the probability distribution of X and P(-1 ≤ X ≤ 2).
Solution:

P(-1 ≤ X ≤ 2) = p(-1) + p(0) + p(1) + p(2)
= 0.2 + 0.15 + 0.10 + 0.10
= 0.55

Question 10.
Find the expected value and variance of the r.v. X if its probability distribution is as follows.
(i)

Solution:

(ii)

Solution:
E(X) = Σx . p(x)

(iii)

Solution:

(iv)

Solution:

= 1.25
S.D. of X = σ_x = √Var(X)
= √1.25
= 1.118

Question 11.
A player tosses two coins. He wins ₹ 10 if 2 heads appear, ₹ 5 if 1 head appears, and ₹ 2 if no head appears. Find the expected value and variance of the winning amount.
Solution:
S : Two fair coin are tossed
S = {HH, HT, TT, TH}
n(S) = 4
∴ Range of X = {0, 1, 2}
∴ Let Y = amount received corresponds to values of X

Expected winning amount
E(Y) = Σpy = \(\frac{22}{4}\) = ₹ 5.5
V(Y) = Σpy² – (Σpy)²
= \(\frac{154}{4}\) – (5.5)²
= 38.5 – 30.25
= ₹ 8.25

Question 12.
Let the p.m.f. of the r.v. X be
\(p(x)= \begin{cases}\frac{3-x}{10} & \text { for } x=-1,0,1,2 \\ 0 & \text { otherwise }\end{cases}\)
Calculate E(X) and Var(X).
Solution:

Question 13.
Suppose error involved in making a certain measurement is a continuous r.v. X with p.d.f.
\(f(x)= \begin{cases}k\left(4-x^{2}\right) & \text { for }-2 \leq x \leq 2 \\ 0 & \text { otherwise }\end{cases}\)
Compute (i) P(X > 0), (ii) P(-1 < X < 1), (iii) P(X < -0.5 or X > 0.5)
Solution:
We know that

Question 14.
The p.d.f. of the r.v. X is given by
\(f(x)= \begin{cases}\frac{1}{2 a} & \text { for } 0<x<2 a \\ 0 & \text { otherwise }\end{cases}\)
Show that P(X < \(\frac{a}{2}\)) = P(X > \(\frac{3a}{2}\))
Solution:

Question 15.
Determine k if
\(f(x)= \begin{cases}k e^{-\theta x} & \text { for } 0 \leq x<\infty, \theta>0 \\ 0 & \text { otherwise }\end{cases}\)
is the p.d.f. of the r.v. X. Also find P(X > \(\frac{1}{\theta}\)). Find M if P(0 < X < M) = \(\frac{1}{2}\)
Solution:
We know that

Question 16.
The p.d.f. of the r.v. X is given by
\(f_{x}(x)=\left\{\begin{array}{l}
\frac{k}{\sqrt{x}}, 0<x<4 \\
0, \text { otherwise }
\end{array}\right.\)
Determine k, c.d.f. of X and hence find P(X ≤ 2) and P(X ≥ 1).
Solution:
We know that

Question 17.
Let X denote the reaction temperature (in °C) of a certain chemical process. Let X be a continuous r.v. with p.d.f.
\(f(x)= \begin{cases}\frac{1}{10}, & -5 \leq x \leq 5 \\ 0, & \text { otherwise }\end{cases}\)
Compute P(X < 0).
Solution:
Given p.d.f. is f(x) = \(\frac{1}{10}\), for -5 ≤ x ≤ 5
Let its c.d.f. F(x) be given by

Part – II

Question 1.
Let X ~ B(10, 0.2). Find (i) P(X = 1) (ii) P(X ≥ 1) (iii) P(X ≤ 8)
Solution:
X ~ B(10, 0.2)
n = 10, p = 0.2
∴ q = 1 – p = 1 – 0.2 = 0.8
(i) P(X = 1) = ¹⁰C₁ (0.2)¹ (0.8)⁹ = 0.2684

(ii) P(X ≥ 1) = 1 – P(X < 1)
= 1 – P(X = 0)
= 1 – ¹⁰C₀ (0.2)⁰ (0.8)¹⁰
= 1 – 0.1074
= 0.8926

(iii) P(X ≤ 8) = 1 – P(x > 1)
= 1 – [p(9) + p(10)]
= 1 – [¹⁰C₉ (0.2)⁹ (0.8)¹ + ¹⁰C₁₀ (0.2)¹⁰]
= 1 – 0.00000041984
= 0.9999

Question 2.
Let X ~ B(n, p) (i) If n = 10 and E(X) = 5, find p and Var(X), (ii) If E(X) = 5 and Var(X) = 2.5, find n and p.
Solution:
X ~ B(n, p)
(i) n = 10, E(X) = 5
∴ np = 5
∴ 10p = 5
∴ p = \(\frac{1}{2}\)
∴ q = 1 – p = 1 – \(\frac{1}{2}\) = \(\frac{1}{2}\)
V(X) = npq
= 10 × \(\frac{1}{2}\) × \(\frac{1}{2}\)
= 2.5

(ii) E(X) = 5, V(X) = 2.5
∴ np = 5, ∴ npq = 2.5
∴ 5q = 2.5
∴ q = \(\frac{2.5}{5}\) = 0.5, p = 1 – 0.5 = 0.5
But np = 5
∴ n(0.5) = 5
∴ n = 10

Question 3.
If a fair coin is tossed 4 times, find the probability that it shows (i) 3 heads, (ii) head in the first 2 tosses, and tail in the last 2 tosses.
Solution:
n : No. of times a coin is tossed
∴ n = 4
X : No. of heads
P : Probability of getting heads

Question 4.
The probability that a bomb will hit the target is 0.8. Find the probability that, out of 5 bombs, exactly 2 will miss the target.
Solution:
X : No. of bombs miss the target
p : Probability that bomb miss the target
∴ q = 0.8
∴ p = 1 – q = 1 – 0.8 = 0.2
n = No. of bombs = 5
∴ X ~ B(5, 0.2)
∴ p(x) = ⁿC_x p^x q^n-x
P(X = 2) = ⁵C₂ (0.2)² (0.8)^5-2
= 10 × 0.04 × (0.8)³
= 10 × 0.04 × 0.512
= 0.4 × 0.512
= 0.2048

Question 5.
The probability that a lamp in the classroom will burn is 0.3. 3 lamps are fitted in the classroom. The classroom is unusable if the number of lamps burning in it is less than 2. Find the probability that the classroom can not be used on a random occasion.
Solution:
X : No. of lamps not burning
p : Probability that the lamp is not burning
∴ q = 0.3
∴ p = 1 – q = 1 – 0.3 = 0.7
n = No. of lamps fitted = 3
∴ X ~ B(3, 0.7)
∴ p(x) = ⁿC_x p^x q^n-x
P(classroom cannot be used)
P(X < 2) = p(0) + p(1)
= ³C₀ (0.7)⁰ (0.3)^3-0 + ³C₁ (0.7)¹ (0.3)^3-1
= 1 × 1 × (0.3)³ + 3 × 0.7 × (0.3)²
= (0.3)2 [0.3 + 3 × 0.7]
= 0.09 [0.3 + 2.1]
= 0.09 [2.4]
= 0.216

Question 6.
A large chain retailer purchases an electric device from the manufacturer. The manufacturer indicates that the defective rate of the device is 10%. The inspector of the retailer randomly selects 4 items from a shipment. Find the probability that the inspector finds at most one defective item in the 4 selected items.
Solution:
X : No. of defective items
n : No. of items selected = 4
p : Probability of getting defective items
∴ p = 0.1
∴ q = 1 – p = 1 – 0.1 = 0.9
P(At most one defective item)
P(X ≤ 1) = p(0) + p(1)
= ⁴C₀ (0.1)⁰ (0.9)^4-0 + ⁴C₁ (0.1)¹ (0.9)^4-1
= 1 × 1 × (0.9)⁴ + 4 × 0.1 × (0.9)³
= (0.9)3 [0.9 + 4 × 0.1]
= (0.9)3 × [0.9 + 0.4]
= 0.729 × 1.3
= 0.9477

Question 7.
The probability that a component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 components tested survive.
Solution:
p = 0.6, q = 1 – 0.6 = 0.4, n = 4
x = 2
∴ p(x) = ⁿC_x p^x q^n-x
P(X = 2) = ⁴C₂ (0.6)² (0.4)² = 0.3456

Question 8.
An examination consists of 5 multiple choice questions, in each of which the candidate has to decide which one of 4 suggested answers is correct. A completely unprepared student guesses each answer randomly. Find the probability that this student gets 4 or more correct answers.
Solution:
n : No. of multiple-choice questions
∴ n = 5
X : No. of correct answers
p : Probability of getting correct answer
∵ There are 4 options out of which one is correct
∴ p = \(\frac{1}{4}\)
∴ q = 1 – p = 1 – \(\frac{1}{4}\) = \(\frac{3}{4}\)
∵ X ~ B(5, \(\frac{1}{4}\))
∴ p(x) = ⁿC_x p^x q^n-x
P(Four or more correct answers)
P(X ≥ 4) = p(4) + p(5)

Question 9.
The probability that a machine will produce all bolts in a production run with in the specification is 0.9. A sample of 3 machines is taken at random. Calculate the probability that all machines will produce all bolts in a production run within the specification.
Solution:
n : No. of samples selected
∴ n = 3
X : No. of bolts produce by machines
p : Probability of getting bolts
∴ p = 0.9
∴ q = 1 – p = 1 – 0.9 = 0.1
∴ X ~ B(3, 0.9)
∴ p(x) = ⁿC_x p^x q^n-x
P(Machine will produce all bolts)
P(X = 3) = ³C₃ (0.9)³ (0.1)^3-3
= 1 × (0.9)³ × (0.1)⁰
= 1 × (0.9)³ × 1
= (0.9)³
= 0.729

Question 10.
A computer installation has 3 terminals. The probability that anyone terminal requires attention during a week is 0.1, independent of other terminals. Find the probabilities that (i) 0 (ii) 1 terminal requires attention during a week.
Solution:
n : No. of terminals
∴ n = 3
X : No. of terminals need attention
p : Probability of getting terminals need attention
∴ p = 0.1
∴ q = 1 – p = 1 – 0.1 = 0.9
∵ X ~ B(3, 0.1)
∴ p(x) = ⁿC_x p^x q^n-x
(i) P(No attention)
∴ P(X = 0) = ³C₀ × (0.1)⁰ (0.9)^3-1
= 1 × 1 × (0.9)³
= 0.729

(ii) P(One terminal need attention)
∴ P(X = 1) = ³C₁ (0.1)¹ (0.9)^3-1
= 3 × 0.1 × (0.9)²
= 0.3 × 0.81
= 0.243

Question 11.
In a large school, 80% of the students like mathematics. A visitor asks each of 4 students, selected at random, whether they like mathematics, (i) Calculate the probabilities of obtaining an answer yes from all of the selected students, (ii) Find the probability that the visitor obtains the answer yes from at least 3 students.
Solution:
X : No. of students like mathematics
p: Probability that students like mathematics
∴ p = 0.8
∴ q = 1 – p = 1 – 0.8 = 0.2
n : No. of students selected
∴ n = 4
∵ X ~ B(4, 0.8)
∴ p(x) = ⁿC_x p^x q^n-x
(i) P(All students like mathematics)
∴ P(X = 4) = ⁴C₄ (0.8)⁴ (0.2)^4-4
= 1 × (0.8)⁴ × (0.2)⁰
= 1 × (0.8)⁴ × 1
= 0.4096

(ii) P(Atleast 3 students like mathematics)
∴ P(X ≥ 3) = p(3) + p(4)
= ⁴C₃ (0.8)³ (0.2)^4-3 + 0.4096
= 4 × (0.8)³ (0.2)¹ + 0.4096
= 0.8 × (0.8)³ + 0.4096
= (0.8)⁴ × 0.4096
= 0.4096 + 0.4096
= 0.8192

Question 12.
It is observed that it rains on 10 days out of 30 days. Find the probability that
(i) it rains on exactly 3 days of a week.
(ii) it rains at most 2 days a week.
Solution:
X : No. of days it rains in a week
p : Probability that it rains
∴ p = \(\frac{10}{30}=\frac{1}{3}\)
∴ q = 1 – p = 1 – \(\frac{1}{3}\) = \(\frac{2}{3}\)
n : No. of days in a week
∴ n = 7
∴ X ~ B(7, \(\frac{1}{3}\))
(i) P(Rains on Exactly 3 days of a week)

(ii) P(Rains on at most 2 days of a week)
∴ P(X ≤ 2) = p(0) + p(1) + p(2)

Question 13.
If X follows Poisson distribution such that P(X = 1) = 0.4 and P(X = 2) = 0.2, find variance of X.
Solution:
X : Follows Possion Distribution

∴ m = 1
∴ Mean = m = Variance of X = 1

Question 14.
If X has Poisson distribution with parameter m, such that
\(\frac{P(X=x+1)}{P(X=x)}=\frac{m}{x+1}\)
find probabilities P(X = 1) and P(X = 2), when X follows Poisson distribution with m = 2 and P(X = 0) = 0.1353.
Solution:
Given that the random variable X follows the Poisson distribution with parameter m = 2
i.e. X ~ P(2)
Its p.m.f. is satisfying the given equation.
\(\frac{P(X=x+1)}{P(X=x)}=\frac{m}{x+1}\)
When x = 0,
\(\frac{\mathrm{P}(\mathrm{X}=1)}{\mathrm{P}(\mathrm{X}=0)}=\frac{2}{0+1}\)
P(X = 1) = 2P(X = 0)
= 2(0.1353)
= 0.2706
When x = 1,
\(\frac{\mathrm{P}(\mathrm{X}=2)}{\mathrm{P}(\mathrm{X}=1)}=\frac{2}{1+1}\)
P(X = 2) = P(X = 1) = 0.2706

12th Commerce Maths Digest Pdf

• 12th Commerce Maths Exercise 8.1 Solutions
• 12th Commerce Maths Exercise 8.2 Solutions
• 12th Commerce Maths Exercise 8.3 Solutions
• 12th Commerce Maths Exercise 8.4 Solutions
• 12th Commerce Maths Miscellaneous Exercise 8 Solutions

Probability Distributions Class 12 Commerce Maths 2 Chapter 8 Exercise 8.4 Answers Maharashtra Board

Balbharati Maharashtra State Board 12th Commerce Maths Solution Book Pdf Chapter 8 Probability Distributions Ex 8.4 Questions and Answers.

Std 12 Maths 2 Exercise 8.4 Solutions Commerce Maths

Question 1.
If X has Poisson distribution with m = 1, then find P(X ≤ 1) given e^-1 = 0.3678.
Solution:
∵ m = 1
∵ X follows Poisson Distribution

= e^-m × 1 + e^-m × 1
= e^-1 + e^-1
= 2 × e^-1
= 2 × 0.3678
= 0.7356

Question 2.
If X ~ P(\(\frac{1}{2}\)), then find P(X = 3) given e^-0.5 = 0.6065.
Solution:

Question 3.
If X has Poisson distribution with parameter m and P(X = 2) = P(X = 3), then find P(X ≥ 2). Use e^-3 = 0.0497
Solution:
∵ X follows Poisson Distribution

Question 4.
The number of complaints which a bank manager receives per day follows a Poisson distribution with parameter m = 4. Find the probability that the manager receives (i) only two complaints on a given day, (ii) at most two complaints on a given day. Use e^-4 = 0.0183.
Solution:
∵ m = 1
∵ X ~ P(m = 4)
∴ p(x) = \(\frac{e^{-m} \cdot m^{x}}{x !}\)
X = No. of complaints recieved
(i) P(Only two complaints on a given day)

(ii) P(Atmost two complaints on a given day)
P(X ≤ 2) = p(0) + p(1) + p(2)
= \(\frac{e^{-4} \times 4^{0}}{0 !}+\frac{e^{-4} \times 4^{1}}{1 !}\) + 0.1464
= e^-4 + e^-4 × 4 + 0.1464
= e^-4 [1 + 4] + 0.1464
= 0.0183 × 5 + 0.1464
= 0.0915 + 0.1464
= 0.2379

Question 5.
A car firm has 2 cars, which are hired out day by day. The number of cars hired on a day follows a Poisson distribution with a mean of 1.5. Find the probability that
(i) no car is used on a given day.
(ii) some demand is refused on a given day, given e^-1.5 = 0.2231.
Solution:
Let X = No. of demands for a car on any day
∴ No. of cars hired
n = 2
m = 1.5
∵ X ~ P(m = 1.5)

Question 6.
Defects on plywood sheets occur at random with an average of one defect per 50 sq. ft. Find the probability that such a sheet has (i) no defect, (ii) at least one defect. Use e^-1 = 0.3678.
Solution:
∵ X = No. of defects on a plywood sheet
∵ m = -1
∵ X ~ P(m = -1)
∴ p(x) = \(\frac{e^{-m} \cdot m^{x}}{x !}\)
(i) P(No defect)
P(X = 0) = \(\frac{e^{-1} \times 1^{0}}{0 !}\)
= e^-1
= 0.3678

(ii) P(At least one defect)
P(X ≥ 1) = 1 – P(X < 1)
= 1 – p(0)
= 1 – 0.3678
= 0.6322

Question 7.
It is known that, in a certain area of a large city, the average number of rats per bungalow is five. Assuming that the number of rats follows Poisson distribution, find the probability that a randomly selected bungalow has
(i) exactly 5 rats
(ii) more than 5 rats
(iii) between 5 and 7 rats, inclusive. Given e^-5 = 0.0067.
Solution:
X = No. of rats
∵ m = 5
∴ X ~ P(m = 5)
∴ p(x) = \(\frac{e^{-m} \cdot m^{x}}{x !}\)
(i) P(Exactly five rats)

(ii) P(More than five rats)
P(X > 5) = 1 – P(X ≤ 5)

(iii) P(between 5 and 7 rats, inclusive)
P(5 ≤ x ≤ 7) = p(5) + p(6) + p(7)

= 0.0067 × 3125 × 0.02
= 0.0067 × 62.5
= 0.42

12th Commerce Maths Digest Pdf

• 12th Commerce Maths Exercise 8.1 Solutions
• 12th Commerce Maths Exercise 8.2 Solutions
• 12th Commerce Maths Exercise 8.3 Solutions
• 12th Commerce Maths Exercise 8.4 Solutions
• 12th Commerce Maths Miscellaneous Exercise 8 Solutions