# Maharashtra Board 12th Commerce Maths Solutions Chapter 2 Insurance and Annuity Ex 2.1

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

## Maharashtra State Board 12th Commerce Maths Solutions Chapter 2 Insurance and Annuity Ex 2.1

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
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
∴ 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
∴ 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
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
∴ 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