Class 7

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 48 Answers Solutions Chapter 13 Pythagoras Theorem.

Pythagoras Theorem Class 7 Practice Set 48 Answers Solutions Chapter 13

Question 1.
In the figures below, find the value of ‘x’.

Solution:
i. In ∆LMN, ∠M = 90°.
Hence, side LN is the hypotenuse.
According to Pythagoras’ theorem,
l(LN)² = l(LM)² + l(MN)²
∴ x² = 72 + 24²
∴ x² = 49 + 576
∴ x² = 625
∴ x² = 25²
∴ x = 25 units

ii. In ∆PQR, ∠Q = 90°.
Hence, side PR is the hypotenuse.
According to Pythagoras’ theorem,
l(PR)² = l(PQ)² + l(QR)²
∴ 412 = 92 + x²
∴ 1681 = 81 + x²
∴ 1681 – 81 = x²
∴ 1600 = x²
∴ x² = 1600
∴ x² = 40²
∴ x = 40 units

iii. In AEDF, ∠D = 90°.
Hence, side EF is the hypotenuse.
According to Pythagoras’ theorem,
l(EF)² = l(ED)² + l(DF)²
∴ 17² = x² + 8²
∴ 289 = x² + 64
∴ 289 – 64 = x²
∴ 225 = x²
∴ x² = 225
∴ x² = 15²
∴ x = 15 units

Question 2.
In the right-angled ∆PQR, ∠P = 90°. If l(PQ) = 24 cm and l(PR) = 10 cm, find the length of seg QR.
Solution:

In ∆PQR, ∠P = 90°.
Hence, side QR is the hypotenuse.
According to Pythagoras’ theorem,
l(QR)² = l(PR)² + l(PQ)²
∴ l(QR)² = 10² + 24²
∴ l(QR)² = 100 + 576
∴ l(QR)² =676
∴ l(QR)² = 26²
∴ l(QR) = 26 cm
∴ The length of seg QR is 26 cm.

Question 3.
In the right-angled ∆LMN, ∠M = 90°. If l(LM) = 12 cm and l(LN) = 20 cm, find the length of seg MN.
Solution:

In ∆LMN, ∠M = 90°.
Hence, side LN is the hypotenuse.
According to Pythagoras’ theorem,
l(LN)² = l(LM)² + l(MN)²
∴ 20² = 12² + l(MN)²
∴ l(MN)² = 20² – 12²
∴ l(MN)² = 400 – 144
∴ l(MN)² = 256
∴ l(MN)² = 16²
∴ l(MN)= 16 cm
∴ The length of seg MN is 16 cm.

Question 4.
The top of a ladder of length 15 m reaches a window 9 m above the ground. What is the distance between the base of the wall and that of the ladder?
Solution:

The wall and the ground are perpendicular to each other. Hence, the ladder leaning against the wall forms a right-angled triangle.
In ∆ABC, ∠B = 90°
According to Pythagoras’ theorem,
l(AC)² = l(AB)² + l(BC)²
∴ 15² = l(BC)² + 9²
∴ 225 = l(BC)² + 81
∴ 225 – 81 = l(BC)²
∴ 144 = l(BC)²
∴ 12² = l(BC)²
∴ l(BC) = 12
∴ The distance between the base of the wall and that of the ladder is 12 m.

Maharashtra Board Class 7 Maths Chapter 13 Pythagoras’ Theorem Practice Set 48 Intext Questions and Activities

Question 1.
Write the name of the hypotenuse of each of the right angled triangles shown below.
i.

The hypotenuse of ∆ABC is__
ii.

The hypotenuse of ∆LMN is__
iii.

The hypotenuse of ∆XYZ is__
Solution:
i. AC
ii. MN
iii. XZ

Question 2.
Draw right-angled triangles with the lengths of hypotenuse and one side as shown in the rough figures below. Measure the third side. Verify the Pythagoras’ theorem. (Textbook pg. no. 87)

Solution:

i. From the figure, by measurement,
l(AB) = 4 cm
Now, in right-angled triangle ABC,
l(AB)² + l(BC)² = (4)² + (3)²
= 16 + 9
∴ l(AB)² + l(BC)² = 25 …. (i)
l(AC)² = (5)² = 25 ….(ii)
∴ From (i) and (ii),
l(AC)² = l(AB)² + l(BC)²
∴ Pythagoras’ theorem is verified.
(Students should draw the triangles PQR and XYZ and verify the Pythagoras ’ theorem)

Question 3.
Without using a protractor, can you verify that every angle of the vacant quadrilateral in the adjacent figure is a right angle? (Textbook pg. no. 89)
Solution:

In the square ABCD the shaded triangles are right-angled and are the same.
In ∆LBM,
m∠BLM + m∠BML + m∠LBM = 180° …. (Sum of the measures of the angles of a triangles is 180° )
∴ m∠BLM + m∠BML + 90° = 180°
∴ m∠BLM + m∠BML = 90° …. (i)
Now, ∆LBM and ∆LAP are same.
∴ m∠BML = m∠ALP …. (ii)
∴ m∠BLM + m∠ALP = 90° …. IFrom (i) and (ii)l
Now, m∠ALP + m∠PLM + m∠BLM = 180° …. (The measure of a straight angle is 180°)
∴ m∠ALP + m∠BLM + m∠PLM = 180°
∴ 90° + m∠PLM = 180°
∴ m∠PLM = 180°- 90° = 90°
∴ m∠PLM is a right angle.
Similarly, we can prove that the other angles of the vacant quadrilateral are right angles.

Question 4.
On a sheet of card paper, draw a right-angled triangle of sides 3 cm, 4 cm and 5 cm. Construct a square on each of the sides. Find the area of each of the squares and verify Pythagoras’ theorem. (Textbook pg. no. 89)
Solution:

Area of square ABLM = l(AB)² = 32 = 9 sq.cm
Area of square BCPN = l(BC)²= 42 = 16 sq.cm
Area of square ACQR = l(AC)² = 52 = 25 sq.cm
Now, 25 = 16 + 9
i.e. 5² = 4² + 3²
∴ l(AC)² = l(BC)² + l(AB)²
∴ (hypotenuse)² = (base)² + (height)²

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 43 Answers Solutions Chapter 11 Circle.

Circle Class 7 Practice Set 43 Answers Solutions Chapter 11

Question 1.
Choose the correct option.
If arc AXB and arc AYB are corresponding arcs and m(arc AXB) = 120° then m(arc AYB) =
(A) 140°
(B) 60°
(C) 240°
(D) 160°
Solution:
(C) 240°

Hint:
Measure of major arc = 360° – measure of corresponding minor arc
∴ m (arc AYB) = 360 – m (arc AXB)
∴ m (arc AYB) = 360 – 120
∴ m (arc AYB) = 240°

Question 2.
Some arcs are shown in the circle with centre ‘O’ Write the names of the minor arcs, major arcs and semicircular arcs from among them.

Solution:
Minor arcs : arc QXP, arc PR, arc RY, arc YQ, arc QX, arc XP, arc PRY.
Major arcs : arc PYQ, arc PQR, arc RQY, arc XPQ, arc XQP, arc XQR
Semicircular arcs : arc QPR, arc QYR.

Question 3.
In a circle with centre O, the measure of a minor arc is 110°. What is the measure of the major arc PYQ?

Solution:
Measure of major arc = 360° – measure of corresponding minor arc
∴ m (arc PYQ) = 360 – 110
∴ m (arc PYQ) = 250°
∴ The measure of the major arc PYQ is 250°.

Maharashtra Board Class 7 Maths Chapter 11 Circle Practice Set 43 Intext Questions and Activities

Question 1.
Measure the circumference and diameter of the objects given below and enter the ratio of the circumference to its diameter in the table.

Examine the ratio of the circumference to the diameter. What do we see? (Textbook pg. no. 75)
Solution:
The ratio of circumference to the diameter is same and is approximately equal to 3.14.

Question 2.
Place a cylindrical bottle on a paper and trace the outline of its base. Use a thread to measure the circumference of the circle. (Textbook pg. no. 75)
Solution:
(Students should attempt the above activities on their own)

Question 3.
Measure the circumference of a bangle with the help of a thread. (Textbook pg. no. 75)
Solution:
(Students should attempt the above activities on their own)

Question 4.
Measure the circumference of any cylindrical object using a thread. (Textbook pg. no. 75)
Solution:
(Students should attempt the above activities on their own)

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 45 Answers Solutions Chapter 12 Perimeter and Area.

Perimeter and Area Class 7 Practice Set 45 Answers Solutions Chapter 12

Question 1.
If the side of a square is 12 cm, find its area.
Solution:
Area of a square = (side)² = (12)²
= 144 sq. cm.
∴ The area of the square is 144 sq. cm.

Question 2.
If the length of a rectangle is 15 cm and breadth is 5 cm, find its area.
Solution:
Area of a rectangle = length × breadth
= 15 × 5
= 75 sq. cm.
∴ The area of the rectangle is 75 sq. cm.

Question 3.
The area of a rectangle is 102 sq. cm. If its length is 17 cm, what is its perimeter?
Solution:
Area of a rectangle = length × breadth
∴ 102 = 17 × breadth
∴ breadth = \(\frac { 102 }{ 17 }\) = 6 cm
Perimeter of rectangle = 2 (length + breadth)
= 2 (17 + 6)
= 2 × 23
= 46 cm
∴ The perimeter of rectangle is 46 cm.

Question 4.
If the side of a square is tripled, how many times will its area be as compared to the area of the original square?
Solution:
Let the side of the square be a.
∴ Area of a square = (side)² = a²
New side of the square = 3 × a = 3a
∴ New area of the square = (3a)²
= 9a²
= 9 × area of original square
∴ If the side of a square is tripled, its area will become 9 times the area of the original square.

Maharashtra Board Class 7 Maths Chapter 12 Perimeter and Area Practice Set 45 Intext Questions and Activities

Question 1.
A rectangular playground is 65m long and 30m wide. A pathway of 1.5 m width goes all around the ground, outside it. Find the area of the pathway. (Textbook pg. no. 82)

Solution:
The playground is rectangular.
₹ABCD is the playground. Around it is a pathway 1.5 m wide.
Around ₹ABCD we get the rectangle ₹PQRS
Length of new rectangle PQRS = 65 + 1.5 + 1.5 = 68 m
Breadth of new rectangle PQRS = 30 + 1.5 + 1.5 = 33m
Area of path = Area of rectangle PQRS – Area of rectangle ABCD = 68 x 33 – 65 x 30
= 2244 – 1950
= 294 sq m

Question 2.
Is there another way to find the area of the pathway in the problem above? (Textbook pg. no. 82)

Solution:
Yes. The area of the pathway can be found by dividing it into rectangles and adding the areas of these rectangles.
Length of rectangle 1 = 30 + 1.5 + 1.5 = 33 m
Breadth of rectangle 1 = 1.5 m
∴ Area of rectangle 1 = 33 x 1.5
= 49.5 sq. m
Area of rectangle 4 = Area of rectangle 1
= 49.5 sq. m.
Length of rectangle 2 = 65 m
breadth of rectangle 2 = 1.5 m
∴ Area of rectangle 2 = 65 x 1.5
= 97.5 sq. m.
Area of rectangle 3 = area of rectangle 2
= 97.5 sq. m.
∴ Area of pathway = Sum of area of the 4 rectangles = 49.5 + 49.5 + 97.5 + 97.5
= 294 sq. m.

Question 3.
The length and the width of a mobile phone are 13 cm and 7 cm respectively. It has a screen PQRS as shown in the figure. What is the area of the screen? (Textbook pg. no. 82)

Solution:
ABCD is the rectangle formed by the edges of the mobile. PQRS is the rectangle formed by leaving a 1.5 cm wide edge alongside AB, BC, and DC, and a 2 cm edge alongside DA.
Length of rectangle PQRS = 9.5 cm
Breadth of rectangle PQRS = 4 cm
Area of screen = Area of rectangle PQRS = 9.5 x 4
= 38 sq .cm

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 47 Answers Solutions Chapter 12 Perimeter and Area.

Perimeter and Area Class 7 Practice Set 47 Answers Solutions Chapter 12

Question 1.
Find the total surface area of cubes having the following sides:
i. 3 cm
ii. 5 cm
iii. 7.2 m
iv. 6.8 m
v. 5.5 m
Solution:
i. Total surface area of cube = 6l²
= 6 × (3)²
= 6 × 9
= 54 sq. cm.

ii. Total surface area of cube = 6l²
= 6 × 5²
= 6 × 25
= 150 sq. cm.

iii. Total surface area of cube = 6l²
= 6 × (7.2)²
= 6 × 51.84
= 311.04 sq. m.

iv. Total surface area of cube = 6l²
= 6 × (6.8)²
= 6 × 46.24
= 277.44 sq. m.

v. Total surface area of cube = 6l²
= 6 × (5.5)²
= 6 × 30.25
= 181.5 sq. m.

Question 2.
Find the total surface area of the cuboids of length, breadth and height as given below:
i. 12 cm, 10 cm, 5 cm
ii. 5 cm, 3.5 cm, 1.4 cm
iii. 2.5 m, 2 m, 2.4 m
iv. 8 m, 5 m, 3.5 m
Solution:
i. Total surface area of cuboid
= 2 (lb + bh + lh)
= 2 (12 × 10 + 10 × 5 + 12 × 5)
= 2 (120 + 50 + 60)
= 2 × 230
= 460 sq. cm.

ii. Total surface area of cuboid
= 2 (lb + bh + lh)
= 2 (5 × 3.5 + 3.5 × 1.4 + 5 × 1.4)
= 2(17.5 + 4.9 + 7)
= 2 × 29.4
= 58.8 sq. cm.

iii. Total surface area of cuboid = 2 (lb + bh + lh)
= 2(2.5 × 2 + 2 × 2.4 + 2.5 × 2.4)
= 2 (5 + 4.8 + 6)
= 2 × 15.8
= 31.6 sq. m.

iv. Total surface area of cuboid = 2 (lb + bh + lh)
= 2 (8 × 5+ 5 × 3.5 + 8 × 3.5)
= 2(40 + 17.5 + 28)
= 2 × 85.5
= 171 sq. m.

Question 3.
A matchbox is 4 cm long, 2.5 cm broad and 1.5 cm in height. Its outer sides are to be covered exactly with craft paper. How much paper will be required to do so?
Solution:
Length of the matchbox (l) = 4 cm, breadth (b) = 2.5 cm, height (h) = 1.5 cm
∴ Total surface area of the matchbox = 2 (lb + bh + lh)
= 2 (4 × 2.5 + 2.5 × 1.5 + 4 × 1.5)
= 2 (10 + 3.75 + 6)
= 2 × 19.75
= 39.5 sq. cm.
∴ 39.5 sq. cm paper will be required.

Question 4.
An open box of length 1.5 m, breadth 1 m, and height 1 m is to be made for use on a trolley for carrying garden waste. How much sheet metal will be required to make this box? The inside and outside surface of the box is to be painted with rust proof paint. At a rate of Rs 150 per sq. m, how much will it cost to paint the box?
Solution:
Length of the box (l) = 1.5 m, breadth (b) = 1 m, height (h) = 1 m
Since, the box is open at top,
∴ Sheet required to make the box = total surface area of the box – area of the top
= 2 (lb + bh + lh) – lb
= 2lb + 2bh + 2lh – lb
= lb + 2bh + 2lh
= 1.5 × 1 + 2 × 1 × 1 + 2 × 1.5 × 1
= 1.5 + 2 + 3
= 6.5 sq. m.
Since, the inside and outside surface of the box are to be painted.
∴ Area to be painted = 2 × Area of the box = 2 × 6.5 = 13 sq. m.
Total cost of painting = area to be painted × rate per sq. m.
= 13 × 150
= Rs 1950
∴ 6.5 sq. m. sheet of metal will be required and the cost of painting the box will be Rs 1950.

Maharashtra Board Class 7 Maths Chapter 12 Perimeter and Area Practice Set 47 Intext Questions and Activities

Question 1.
Measure the length and breadth of the courts laid out for games such as kho-kho, kabaddi, tennis, badminton, etc. Find out their perimeters and areas. (Textbook pg. no. 81)
Solution:
(Students should attempt the above activities on their own)

Question 2.
Take mobile handsets of different sizes and find the area of their screens. (Textbook pg. no. 82)
Solution:
(Students should attempt the above activities on their own)

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 46 Answers Solutions Chapter 12 Perimeter and Area.

Perimeter and Area Class 7 Practice Set 46 Answers Solutions Chapter 12

Question 1.
A page of a calendar is 45 cm long and 26 cm wide. What is its area?
Solution:
Area of page of a calendar = length × breadth
= 45 × 26
= 1170 sq. cm.
∴ The area of the page of the calendar is 1170 sq. cm.

Question 2.
What is the area of a triangle with base 4.8 cm and height 3.6 cm?
Solution:
Area of triangle = \(\frac { 1 }{ 2 }\) × base × height
= \(\frac { 1 }{ 2 }\) × 4.8 × 3.6
= \(\frac { 1 }{ 2 }\) × 17.28
= 8.64 sq. cm.
∴ The area of the triangle is 8.64 sq. cm.

Question 3.
What is the value of a rectangular plot of land 75.5 m long and 30.5 m broad at the rate of Rs 1000 per square metre?
Solution:
Area of the rectangular plot = length × breadth
= 75.5 × 30.5
= 2302.75 sq. m.
Value of the plot = area of the plot × rate per square metre = 2302.75 × 1000
= Rs 230275
∴ The value of the plot is Rs 23,02,750.

Question 4.
A rectangular hall is 12 m long and 6 m broad. Its flooring is to be made of square tiles of side 30 cm. How many tiles will fit in the entire hall? How many would be required if tiles of side 15 cm were used?
Solution:
Area of the rectangular hall = length × breadth
= 12 × 6
= 72 sq. m.
Side of the square shaped tile = 30 cm
= \(\frac { 30 }{ 100 }\) m …[1cm = \(\frac { 1 }{ 100 }\)m]
= \(\frac { 3 }{ 10 }\) m
Area of the tile = (side)²
= \(\left(\frac{3}{10}\right)^{2}\)
= \(\frac{9}{100}\) sq.m
Number of tiles required = \(\frac{\text { Area of the hall }}{\text { Area of each tile }}\)
= \(72 \div \frac{9}{100}\)
= \(72 \times \frac{100}{9}\)
= 800
∴ 800 square shaped tiles of 30 cm side will be required.
If the side of the square is reduced to half, its area will become \(\frac { 1 }{ 4 }\) times the original.
i. e. number of tiles required will become 4 times the original tiles.
∴ Number of tiles required = 4 × number of tiles of side 30 cm
= 4 × 800
= 3200
∴ 3200 square shaped tiles of 15 cm side will be required.

Question 5.
Find the perimeter and area of a garden with measures as shown in the figure alongside.

Solution:

The boundary of the garden is made of 12 sides each of length 13 m.
Perimeter of the garden = sum of the lengths of all sides
= 12 × 13
= 156 m
The garden in the given figure can be divided into 5 squares each of side 13 m.
∴ Area of the garden = 5 × area of each square part
= 5 × (side)²
= 5 × (13)²
= 5 × 169
= 845 sq. m.
∴ The perimeter and area of a garden are 156 m and 845 sq. m. respectively.

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 42 Answers Solutions Chapter 11 Circle.

Circle Class 7 Practice Set 42 Answers Solutions Chapter 11

Question 1.
Complete the table below:

Sr. No	Radius (r)	Diameter (d)	Circumference (c)
i.	7 cm
ii.		28 cm
iii.			616 cm
iv.			72.6 cm

Solution:
i. Radius (r) = 7 cm
Diameter (d) = 2r
= 2 x 7 = 14 cm
Circumference (c) = πd
= \(\frac { 22 }{ 7 }\) x 14
= 44 cm

ii. Diameter (d) = 28 cm
Radius (r) = \(\frac{d}{2}=\frac{28}{2}\) = 14 cm
Circumference (c) = πd
= \(\frac { 22 }{ 7 }\) x 28
= 88 cm

iii. Circumference (c) = 616 cm
∴ πd = 616
∴ \(\frac { 22 }{ 7 }\) x d = 616
∴ d = 616 x \(\frac { 7 }{ 22 }\)
∴ d = 196 cm
∴ Diameter (d) = 196 cm
Radius (r) = \(\frac{\mathrm{d}}{2}=\frac{196}{2}\) = 98 cm

iv. Circumference (c) = 72.6 cm
∴ πd = 72.6
\(\frac { 22 }{ 7 }\) x d = 72.6
∴ \(d=72.6 \times \frac{7}{22}=\frac{726}{10} \times \frac{7}{22}=\frac{33 \times 7}{10}\)
∴ d = 23.1 cm
∴ Diameter (d) = 23.1 cm
Radius (r) = \(\frac{\mathrm{d}}{2}=\frac{23.1}{2}\)
= 11.55 cm

Sr. No	Radius (r)	Diameter (d)	Circumference (c)
i.	7 cm	14 cm	44 cm
ii.	14 cm	28 cm	88 cm
iii.	98 cm	196 cm	616 cm
iv.	11.55 cm	23.1 cm	72.6 cm

Question 2.
If the circumference of a circle is 176 cm, find its radius.
Solution:
Circumference (c) = 176 cm
∴ 2πr = 176
∴ 2 x \(\frac { 22 }{ 7 }\) x r = 176
∴ \(\frac { 44 }{ 7 }\) x r = 176
∴ r = 176 x \(\frac { 7 }{ 44 }\) = 28 cm
∴ The radius of the circle is 28 cm.

Question 3.
The radius of a circular garden is 56 m. What would it cost to put a 4-round fence around this garden at a rate of 40 rupees per metre?
Solution:
Radius of the circular garden (r) = 56 m
∴ Circumference of the circular garden (c) = 2πr
= 2 x \(\frac { 22 }{ 7 }\) x 56
= 352 m
∴ Length of the wire required to put 1-round fence = Circumference
∴ Length of wire required to put a 4-round fence = 4 x Circumference
= 4 x 352
= 1408 m
∴ Cost of wire per meter = Rs 40
∴ Total cost = length of wire required x cost of the wire
= 1408 x 40
= Rs 56320
∴ The cost to put a 4-round fence around the garden is Rs 56320.

Question 4.
The wheel of a bullock cart has a diameter of 1.4 m. How many rotations will the wheel complete as the cart travels 1.1 km?
Solution:
Diameter of the wheel of the bullock cart (d) = 1.4 m
Circumference of the wheel of the bullock cart (c) = πd
\(=\frac{22}{7} \times 1.4=\frac{22}{7} \times \frac{14}{10}=\frac{44}{10}=4.4 \mathrm{m}\)
Distance covered in 1 rotation = Circumference of the wheel
= 4.4 m

∴ The wheel of the bullock cart will complete 250 rotations as the cart travels 1.1 km.

Maharashtra Board Class 7 Maths Chapter 11 Circle Practice Set 42 Intext Questions and Activities

Question 1.
Identify the radii, chords and diameters in the circle alongside and write their names in the table below: (Textbook pg. no. 75)

i. Radii
ii. Chords
iii. Diameters

Solution:
i. OA, OB, OC, OF
ii. EC, AD, AB, FC
iii. AB, FC

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 44 Answers Solutions Chapter 12 Perimeter and Area.

Perimeter and Area Class 7 Practice Set 44 Answers Solutions Chapter 12

Question 1.
If the length and breadth of a rectangle are doubled, how many times the perimeter of the old rectangle will that of the new rectangle be?
Solution:
Let the length of the old rectangle be l and breadth be b.
∴ Perimeter of old rectangle = 2(l + b)
Length of new rectangle = 2l and breadth = 2b
∴ Perimeter of new rectangle = 2(2l + 2b)
= 2 x 2 (l + b)
= 2 x perimeter of old rectangle
∴ The perimeter of new rectangle will be twice the perimeter of old rectangle.

Question 2.
If the side of a square is tripled, how many times the perimeter of the first square will that of the new square be?
Solution:
Let the length of the square be a.
Perimeter of square = 4 x side
= 4 x a = 4a
Side of new square = 3 x a = 3a
Perimeter of new square = 4 x side
= 4 x 3a = 3 x 4a = 3x perimeter of original square.
∴ The perimeter of new square will be three times the perimeter of original square.

Question 3.
Given alongside is the diagram of a playground. It shows the length of its sides. Find the perimeter of the playground.

Solution:

Side AF = side BC + side DE
∴ Side AF = 15 + 15 = 30 m
Side FE = side AB + side CD
∴ Side FE = 10 + 5 = 15 m
∴ Perimeter of the playground = side AB + side BC + side CD + side DE + side FE + side AF
= 10 + 15 + 5 + 15 + 15 + 30
= 90 m.
∴ The perimeter of the playground is 90 m.

Question 4.
As shown in the figure, four napkins all of the same size were made from a square piece of cloth of length 1 m. What length of lace will be required to trim all four sides of all the napkins?

Solution:
Side of the square piece of cloth = 1 m
∴ Side of each napkin = 0.5 m
Length of lace that will be required for 1 napkin = perimeter of the napkin
= 4 x side = 4 x 0.5 = 2 m
∴ Perimeter of 4 napkins = 4 x 2 = 8 m
∴ 8 metre long lace will be required to trim all four napkins.

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 41 Answers Solutions Chapter 10 Bank and Simple Interest.

Bank and Simple Interest Class 7 Practice Set 41 Answers Solutions Chapter 10

Question 1.
If the interest on Rs 1700 is Rs 340 for 2 years, the rate of interest must be__.
(A) 12%
(B) 15%
(C) 4%
(D) 10%
Solution:
(D) 10%

Hint:
∴ \(\text { Total interest }=\frac{P \times R \times T}{100}\)
∴ \(340=\frac{1700 \times R \times 2}{100}\)
∴ R = 10%

Question 2.
If the interest on Rs 3000 is Rs 600 at a certain rate for a certain number of years, what would the interest be on Rs 1500 under the same conditions?
(A) Rs 300
(B) Rs 1000
(C) Rs 700
(D) Rs 500
Solution:
(A) Rs 300

Hint:
The interest on Rs 3000 at certain rate of interest is Rs 600.
Let us suppose the interest on Rs 1500 at the same rate is x.
∴ \(\frac{600}{3000}=\frac{x}{1500}\)
∴ x = Rs 300

Question 3.
Javed deposited Rs 12000 at 9 p.c.p.a in a bank for some years, and withdrew his interest every year. At the end of the period, he had received altogether Rs 17,400. For how many years had he deposited his money?
Solution:
Here, P = Rs 12000, R = 9 p.c.p.a and amount = Rs 17400
Amount = Principal + Interest
∴17400 = 12000 + Interest
∴Interest = 17400 – 12000 = Rs 5400
∴ \(\text { Total interest }=\frac{P \times R \times T}{100}\)
\(5400=\frac{12000 \times 9 \times \mathrm{T}}{100}\)
∴ \(\frac{5400 \times 100}{12000 \times 9}=\mathrm{T}\)
∴ T = 5 years
∴ Javed had deposited the amount for 5 years.

Question 4.
Lataben borrowed some money from a bank at a rate of 10 p.c.p.a interest for \(2\frac { 1 }{ 2 }\) years to start a cottage industry. If she paid Rs 10250 as total interest, how much money had she borrowed?
Solution:
Here, R = 10 p.c.p.a, T = 2.5 years, I = Rs 10250

∴ P = Rs 41000
∴ Lataben had borrowed an amount of Rs 41000 from the bank.

Question 5.
Fill in the blanks in the table.

	Principal	Rate of interest (p.c.p.a.)	Time	Interest	Amount
i.	Rs 4200	7%	3 years
ii.		6%	4 years	Rs 1200
iii.	Rs 8000	5%		Rs 800
iv.		5%		Rs 6000	Rs 18000
v.		\(2\frac { 1 }{ 2 }\) % 2	5 years	Rs 2400

Solution:
i. \(\text { Total interest }=\frac{P \times R \times T}{100}\)
= \(\frac{4200 \times 7 \times 3}{100}\)
= Rs 882
Amount = Principal + interest
= 4200 + 882
= Rs 5082

ii. \(\text { Total interest }=\frac{P \times R \times T}{100}\)
∴ \(1200=\frac{\mathrm{P} \times 6 \times 4}{100}\)
∴ \(\frac{1200 \times 100}{6 \times 4}=\mathrm{P}\)
∴ P = Rs 5000
Amount = Principal + interest
= 5000 + 1200
= Rs 6200

iii. \(\text { Total interest }=\frac{P \times R \times T}{100}\)
∴ \(800=\frac{8000 \times 5 \times \mathrm{T}}{100}\)
∴ \(\frac{800 \times 100}{8000 \times 5}=\mathrm{T}\)
∴ T = 2 years
Amount = Principal + interest
= 8000 + 800
= Rs 8800

iv. Amount = Principal + interest
∴ 18000 = Principal + 6000
∴ Principal = Rs 12000
\(\text { Total interest }=\frac{P \times R \times T}{100}\)
∴ \(6000=\frac{12000 \times 5 \times \mathrm{T}}{100}\)
∴ \(\frac{6000 \times 100}{12000 \times 5}=\mathrm{T}\)
∴ T = 10 years

v. R = \(2\frac { 1 }{ 2 }\) % = 2.5 %
∴ \(\text { Total interest }=\frac{P \times R \times T}{100}\)
∴ \(2400=\frac{\mathrm{P} \times 2.5 \times 5}{100}\)
∴ \(2400=\frac{P \times 25 \times 5}{100 \times 10}\)
∴ \(\frac{2400 \times 10 \times 100}{25 \times 5}=P\)
∴ P = Rs 19200
Amount = Principal + interest
= 19200 + 2400
= Rs 21600

	Principal	Rate of interest (p.c.p.a.)	Time	Interest	Amount
i.	Rs 4200	7%	3 years	Rs 882	Rs 5082
ii.	Rs 5000	6%	4 years	Rs 1200	Rs 6200
iii.	Rs 8000	5%	2 years	Rs 800	Rs 8800
iv.	Rs 12000	5%	10 years	Rs 6000	Rs 18000
v.	Rs 19200	\(2\frac { 1 }{ 2 }\) % 2	5 years	Rs 2400	Rs 21600

Maharashtra Board Class 7 Maths Chapter 10 Banks and Simple Interest Practice Set 41 Intext Questions and Activities

Question 1.
Ask an adult in your house to show you a passbook and explain the entries made in it. (Textbook pg. no. 70)
Solution:
(Students should attempt the above activities with the help of their parent / teacher.)

Question 2.
Visit different banks and find out the rates of the interest they give for different types of accounts. (Textbook pg. no. 74)
Solution:
(Students should attempt the above activities with the help of their parent / teacher.)

Question 3.
With the help of your teachers, start a Savings Bank in your school and open an account in it to save up some money. (Textbook pg. no. 74)
Solution:
(Students should attempt the above activities with the help of their parent / teacher.)

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 38 Answers Solutions Chapter 9 Direct Proportion and Inverse Proportion.

Direct Proportion and Inverse Proportion Class 7 Practice Set 38 Answers Solutions Chapter 9

Question 1.
Five workers take 12 days to weed a field. How many days would 6 workers take? How many would 15 take?
Solution:
Let 6 workers take x days and 15 workers take y days to weed the field.
The number of workers and the time required to weed the field are in inverse proportion.
∴ 6 × x = 5 × 12
∴ \(x=\frac{5 \times 12}{6}\)
∴ x = 10 days
Also, 15 × y = 5 × 12
∴ \(y=\frac{5 \times 12}{15}\)
= 4 days
∴ 6 workers will take 10 days and 15 workers will take 4 days to weed the field.

Question 2.
Mohanrao took 10 days to finish a book, reading 40 pages every day. How many pages must he read in a day to finish it in 8 days?
Solution:
Let Mohanrao read x pages every day to finish the book in 8 days.
The number of pages read per day and the days required to finish the book are in inverse proportion.
∴ 8 × x = 10 × 40
∴ \(x=\frac{10 \times 40}{8}\)
= 50
∴ Mohanrao will have to read 50 pages every day to finish the book in 8 days.

Question 3.
Mary cycles at 6 km per hour. How long will she take to reach her Aunt’s house which is 12 km away? If she cycles at a speed of 4 km/hr, how long would she take?
Solution:
Speed of the cycle = 6 km / hr
Distance travelled to reach her Aunt’s house = 12 km
∴ \(\text { Time required }=\frac{\text { Distance travelled }}{\text { Speed }}\)
= \(\frac { 12 }{ 6 }\)
= 2 hours
Let the time required when the speed of the cycle is 4 km/hr be x hours.
The speed of the cycle and the time required to travel the same distance are in inverse proportion.
∴ 4 × x = 6 × 2
∴ \(x=\frac{6 \times 2}{4}\) = 3 hours
∴ Mary will require 2 hours if she is cycling at 6 km/hr and 3 hours if she is cycling at 4 km/hr to reach her Aunt’s house.

Question 4.
The stock of grain in a government warehouse lasts 30 days for 4000 people. How many days will it last for 6000 people?
Solution:
Let the stock of grain last for x days for 6000 people.
The number of people and the days for which stock will last are in inverse proportion.
∴ 6000 × x = 4000 × 30
∴ \(x=\frac{4000 \times 30}{6000}=20\)
∴ The stock of grain will last for 20 days for 6000 people.

Maharashtra Board Class 7 Maths Chapter 9 Direct Proportion and Inverse Proportion Practice Set 38 Intext Questions and Activities

Question 1.
Students of a certain school went for a picnic to a farm by bus. Here are some of their experiences. Say whether the quantities in each are in direct or in inverse proportion.
(Textbook pg. no. 65 and 66)
i. Each student paid Rs 60 for the expenses.
As there were 45 students,___rupees were collected.
Had there been 50 students,___rupees would have been collected.
The number of students and money collected are in___proportion.

ii. The sweets shop near the school gave 90 laddoos for the picnic.
If 45 students go for the picnic, each will get___laddoos.
If 30 students go for the picnic, each will get___laddoos.
The number of students and that of laddoos each one gets are in___proportion.

iii. The farm is 120 km away from the school.
The bus went to the farm at a speed of 40 km per hour and took___hours.
On the return trip, the speed was 60 km per hour. Therefore, it took___hours.
The speed of the bus and the time it takes are in___proportion.

iv. The farmer picked 180 bors from his trees.
He gave them equally to 45 students. Each student got___bors.
Had there been 60 students, each would have got___bors.
The number of students and the number of bors each one gets are in___proportion.
Solution:
i. Rs 2700, Rs 3000, direct
ii. 2,3, inverse
iii. 3,2, inverse
iv. 4,3, inverse

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 39 Answers Solutions Chapter 9 Direct Proportion and Inverse Proportion.

Direct Proportion and Inverse Proportion Class 7 Practice Set 39 Answers Solutions Chapter 9

Question 1.
Suresh and Ramesh together invested Rs 144000 in the ratio 4 : 5 and bought a plot of land. After some years they sold it at a profit of 20%. What is the profit each of them got?
Solution:
Total investment = Rs 144000
Profit earned = 20%
∴ Total profit = 20% of 144000 = \(\frac{20}{100} \times 144000\) = Rs 28800
Proportion of investment of Suresh and Ramesh = 4:5
Let the profit of Suresh be Rs 4x and that of Ramesh be Rs 5x.
4x + 5x = 28800
∴ 9x = 28800
∴ \(x=\frac { 28800 }{ 9 }\)
= 3200
∴ Suresh’s profit = 4x = 4 × 3200 = Rs 12800
Ramesh’s profit = 5x = 5 × 3200 = Rs 16000
∴ The profit earned by Suresh and Ramesh are Rs 12800 and Rs 16000 respectively.

Question 2.
Virat and Samrat together invested Rs 50000 and Rs 120000 to start a business. They suffered a loss of 20%. How much loss did each of them incur?
Solution:
Total investment = Rs 50000 + Rs 120000 = Rs 170000
Loss incurred = 20%
∴ Total loss = 20% of 170000 = \(\frac{20}{100} \times 170000\) = Rs 34000
Proportion of investment = 50000 : 120000
= 5 : 12 …. (Dividingby 10000)
Let the loss incurred by Virat be Rs 5x and that by Samrat be Rs 12x.
5x + 12x = 34000
∴ 17x = 34000
∴ \(x=\frac { 34000 }{ 17 }=2000\)
∴ Virat’s loss = 5x = 5 × 2000 = Rs 10000
Samrat’s loss = 12x = 12 × 2000 = Rs 24000
∴ The loss incurred by Virat and Samrat are Rs 10000 and Rs 24000 respectively.

Question 3.
Shweta, Piyush and Nachiket together invested Rs 80000 and started a business of selling sheets and towels from Solapur. Shweta’s share of the capital was Rs 30000 and Piyush’s Rs 12000. At the end of the year they had made a profit of 24%. What was Nachiket’s investment and what was his share of the profit?
Solution:
Total investment = Rs 80000
Nachiket’s investment = Total investment – (Shweta’s investment + Piyush’s investment)
= 80000 – (30000+ 12000)
= 80000 – 42000 = Rs 38000
Profit earned = 24%
∴ Total profit = 24% of 80000 = \(\frac { 24 }{ 100 }\) x 80000 = Rs 19200
Proportion of investment = 30000 : 12000 : 38000
= 15 : 6 : 19 …. (Dividing by 2000)
Let the profit of Shweta, Piyush and Nachiket be Rs 15x, Rs 6x and Rs 19x respectively.
15x + 6x + 19x = 19200
∴ 40x = 19200
∴ \(x=\frac { 19200 }{ 40 }=480\)
∴ Nachiket’s profit = 19x = 19 × 480 = Rs 9120
∴ Nachiket’s investment is Rs 38000 and his profit is Rs 9120.

Question 4.
A and B shared a profit of Rs 24500 in the proportion 3 : 7. Each of them gave 2% of his share of the profit to the Soldiers’ Welfare Fund. What was the actual amount given to the Fund by each of them?
Solution:
Proportion of share = 3:7
Let the profits of A and B be Rs 3x and Rs 7x respectively.
3x + 7x = 24500
∴ 10x = 24500
∴ \(x=\frac { 24500 }{ 10 }=2450\)
Profit earned by A = 3x = 3 × 2450 = Rs 7350
Amount given by A = 2% of his profit
= \(\frac { 2 }{ 100 }\) × 7350 = Rs 147
Profit earned by B = 7x = 7 × 2450 = Rs 17150
Amount given by B = 2% of his profit
= \(\frac { 2 }{ 100 }\) × 17150 = Rs 343
∴ The amount given by A and B to the Soldiers’ Welfare Fund are Rs 147 and Rs 343 respectively.

Question 5.
Jaya, Seema, Nikhil and Neelesh put in altogether Rs 360000 to form a partnership, with their investments being in the proportion 3 : 4 : 7 : 6. What was Jaya’s actual share in the capital? They made a profit of 12%. How much profit did Nikhil make?
Solution:
Total investment = Rs 360000
Profit earned = 12%
∴ Total profit = 12% of 360000
= \(\frac{12}{100} \times 360000\) = Rs 43200
Proportion of investment = 3 : 4 : 7 : 6
Let the investment of Jaya, Seema, Nikhil and Neelesh be Rs 3x, Rs 4x, Rs 7x and Rs 6x respectively.
3x + 4x + 7x + 6x = 360000
∴ 20x = 360000
∴ \(x=\frac { 360000 }{ 20 }\)
= 18000
∴ Jaya’s investment = 3x = 3 x 18000 = Rs 54000
Also, profit made by them is Rs 43200
∴ 3x + 4x + 7x + 6x = 43200
∴ 20x = 43200
∴ \(x=\frac { 43200 }{ 20 }\)
= 2160
∴ Nikhil’s profit = 7x = 7 x 2160 = Rs 15120
∴ Jaya’s share in the capital was Rs 54000 and the profit made by Nikhil was Rs 15120.

Maharashtra Board Class 7 Maths Chapter 9 Direct Proportion and Inverse Proportion Practice Set 39 Intext Questions and Activities

Question 1.
Saritaben, Ayesha and Meenakshi started a business by investing Rs 2400, Rs 5200 and Rs 3400. They made a profit of 50%. If they reinvested all their profit by adding it to the capital, find out the proportions of their shares in the capital during the following year. (Textbook pg. no. 67)
Solution:
Total investment = Rs 2400 + Rs 5200 + Rs 3400 = Rs 11000
Total profit = 50% of 11000 = \(\frac{50}{100} \times 11000\) = Rs 5500
Proportion of shares = 2400 : 5200 : 3400
= 12 : 26 : 17 …. (Dividingby 200)
Let the profit of Saritaben, Ayesha and Meenakshi be Rs 12x, Rs 26x and Rs 17x respectively.
12x + 26x + 17x = 5500
∴ 55x = 5500
∴ x = 100
∴ Saritaben’s profit = 12x = 12 × 100 = Rs 1200
Ayesha’s profit = 26x = 26 × 100 = Rs 2600
Meenakshi’s profit = 17x = 17 × 100 = Rs 1700
∴ Saritaben’s new investment = 2400 + 1200 = Rs 3600
Ayesha’s new investment = 5200 + 2600 = Rs 7800
Meenakshi’s new investment = 3400 + 1700 = Rs 5100
∴ New proportion of shares = 3600 : 7800 : 5100
= 12 : 26 : 17 …. (Dividing by 300)
∴ The proportion of the shares in the capital during the following year is 12 : 26 :17

Question 2.
Are the amount of petrol filled in a motorcycle and the distance traveled by it, in direct proportion? (Textbook pg. no. 63)
Solution:
Yes.
If amount of petrol filled in the motorcycle is less, it will travel less distance and if the amount of petrol filled is more, it will travel more distance.
Hence, the amount of petrol filled in the motorcycle and the distance traveled by it are in direct proportion.

Question 3.
Can you give examples from science or everyday life of quantities that vary in direct proportion? (Textbook pg. no. 63)
Solution:

1. Number of chairs and the number of spectators.
2. Quantity (litres) of water and number of vessels required to store the water.