NCERT Solutions for Class 7 Maths Chapter 7 Comparing Quantities
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Book Name: Maths
Subject: Maths
Chapter Number: 8
Chapter Name: Comparing Quantities
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Book Name: Maths
Subject: Maths
Chapter Number: 8
Chapter Name: Comparing Quantities
You can also bookmark this page by clicking + Save to Library icon and refer to these NCERT Solutions anytime from your account. More Detail
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Page 1
NCERT
SOLUTIONS
CLASS - 7TH
aglase .co
SOLUTIONS
CLASS - 7TH
aglase .co
Page 2
Book : Mathematics Ncert Solutions | Chapter-8 Maths
Class : 7th
Subject : Maths
Chapter : 8
Chapter Name : Comparing Quantities
Exercise 8.1
Q1 Find the ratio of:
(a) Rs.5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hours
Answer. (a) 5 to 50 paise
1 rupee = 100 paise
5 rupee = 500 paise
∴ 50Rs 5
paise
= 500
50
= 10
1
Hence, the required ratio is 10:1.
(b) 15 kg to 210 g
1 Kg = 1000 g
15 kg = 15000 g
15kg
⇒ 210g = 15000
210
= 500
7
Hence, the required ratio is 500:7.
(c) 9 m to 27 cm
1 m = 100 cm
9 m = 900 cm
9cm
⇒ 27cm = 900
27
= 100
3
Hence, the required ratio is 100:3.
(d) 30 days to 36 hours
1 days = 24 hrs
30 days = 24 x 30 = 720 hrs
30 days
⇒ 36hrs
= 720
36
= 20
1
Hence, the required ratio is 20:1.
Page : 157 , Block Name : Exercise 8.1
Q2 In a computer lab, there are 3 computers for every 6 students. How many computers
Page 1 of 11 Aglasem Schools
Class : 7th
Subject : Maths
Chapter : 8
Chapter Name : Comparing Quantities
Exercise 8.1
Q1 Find the ratio of:
(a) Rs.5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hours
Answer. (a) 5 to 50 paise
1 rupee = 100 paise
5 rupee = 500 paise
∴ 50Rs 5
paise
= 500
50
= 10
1
Hence, the required ratio is 10:1.
(b) 15 kg to 210 g
1 Kg = 1000 g
15 kg = 15000 g
15kg
⇒ 210g = 15000
210
= 500
7
Hence, the required ratio is 500:7.
(c) 9 m to 27 cm
1 m = 100 cm
9 m = 900 cm
9cm
⇒ 27cm = 900
27
= 100
3
Hence, the required ratio is 100:3.
(d) 30 days to 36 hours
1 days = 24 hrs
30 days = 24 x 30 = 720 hrs
30 days
⇒ 36hrs
= 720
36
= 20
1
Hence, the required ratio is 20:1.
Page : 157 , Block Name : Exercise 8.1
Q2 In a computer lab, there are 3 computers for every 6 students. How many computers
Page 1 of 11 Aglasem Schools
Page 3
Book : Mathematics Ncert Solutions | Chapter-8 Maths
will be needed for 24 students?
Answer. For 6 students, number of computers required = 3
∴ For 1 student, number of computers required = 36 = 12
∴ For 24 students, number Of computers required = 24 ∗ 12 = 12
Hence, 12 computers are required for 24 students.
Page : 157 , Block Name : Exercise 8.1
Q3 Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs.
2 2
Area of Rajasthan = 3 lakh km and area of UP = 2 lakh km .
2
(i) How many people are there per km in both these States?
(ii) Which State is less populated?
2
Answer. (i) Population Of Rajasthan in 3 km area = 570 lakh
2 570
Population of Rajasthan in 1 km area = 3 = 190lakh
2
Population Of U.P in 2 km area = 1660 lakh
2 1660
Population Of U.P in 1 km area = = 2 = 830lakh
(ii) It can be observed that population per km2 area is lesser for Rajasthan. Therefore,
Rajasthan is less populated.
Page : 157 , Block Name : Exercise 8.1
Exercise 8.2
Q1 Convert the given fractional numbers to per cents.
(a) 18
5
(b) 4
3
(c) 40
(d) 27
Answer.
(a)
1 1 100
= ×
8 8 100
1
= × 100%
8
= 12.5%
Page 2 of 11 Aglasem Schools
will be needed for 24 students?
Answer. For 6 students, number of computers required = 3
∴ For 1 student, number of computers required = 36 = 12
∴ For 24 students, number Of computers required = 24 ∗ 12 = 12
Hence, 12 computers are required for 24 students.
Page : 157 , Block Name : Exercise 8.1
Q3 Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs.
2 2
Area of Rajasthan = 3 lakh km and area of UP = 2 lakh km .
2
(i) How many people are there per km in both these States?
(ii) Which State is less populated?
2
Answer. (i) Population Of Rajasthan in 3 km area = 570 lakh
2 570
Population of Rajasthan in 1 km area = 3 = 190lakh
2
Population Of U.P in 2 km area = 1660 lakh
2 1660
Population Of U.P in 1 km area = = 2 = 830lakh
(ii) It can be observed that population per km2 area is lesser for Rajasthan. Therefore,
Rajasthan is less populated.
Page : 157 , Block Name : Exercise 8.1
Exercise 8.2
Q1 Convert the given fractional numbers to per cents.
(a) 18
5
(b) 4
3
(c) 40
(d) 27
Answer.
(a)
1 1 100
= ×
8 8 100
1
= × 100%
8
= 12.5%
Page 2 of 11 Aglasem Schools
Page 4
Book : Mathematics Ncert Solutions | Chapter-8 Maths
(b)
5 5 100
= ×
4 4 100
500
= % = 125%
4
(c)
3 3 100
= ×
40 40 100
300
= % = 7.5%
40
(d)
2
7
= 27 × 100
100
= 200
7
% = 28 47 %
Page : 164 , Block Name : Exercise 8.2
Q2 Convert the given decimal fractions to per cents.
(a) 0.65 (b) 2.1 (c) 0.02 (d) 12.35
Answer. (a) 0.65
0.65 = 0.65 × 100%
65 × 100
= % = 65%
100
(b) 2.1
2.1 = 2.1 × 100%
21 × 100
= % = 210%
10
(c) 0.02
0.02 = 0.02 × 100%
2 × 100
= % = 2%
100
(d) 12.35
12.35 = 12.35 × 100%
1235 × 100
= % = 1235%
100
Page : 165 , Block Name : Exercise 8.2
Q3 Estimate what part of the �gures is coloured and hence �nd the per cent which is
coloured.
Page 3 of 11 Aglasem Schools
(b)
5 5 100
= ×
4 4 100
500
= % = 125%
4
(c)
3 3 100
= ×
40 40 100
300
= % = 7.5%
40
(d)
2
7
= 27 × 100
100
= 200
7
% = 28 47 %
Page : 164 , Block Name : Exercise 8.2
Q2 Convert the given decimal fractions to per cents.
(a) 0.65 (b) 2.1 (c) 0.02 (d) 12.35
Answer. (a) 0.65
0.65 = 0.65 × 100%
65 × 100
= % = 65%
100
(b) 2.1
2.1 = 2.1 × 100%
21 × 100
= % = 210%
10
(c) 0.02
0.02 = 0.02 × 100%
2 × 100
= % = 2%
100
(d) 12.35
12.35 = 12.35 × 100%
1235 × 100
= % = 1235%
100
Page : 165 , Block Name : Exercise 8.2
Q3 Estimate what part of the �gures is coloured and hence �nd the per cent which is
coloured.
Page 3 of 11 Aglasem Schools
Page 5
Book : Mathematics Ncert Solutions | Chapter-8 Maths
Answer. (i) Here, 1 part out of 4 equal parts are shaded which represents the fraction 14 .
1
4
= 14 × 100% = 25%
(ii) Here, 3 parts out of 5 equal parts are shaded which represents the fraction 35
3
5
= 35 × 100% = 60%
(iii) Here, 3 parts out of 8 equal parts are shaded which represents the fraction 38
3
8
= 38 × 100% = 300
8
% = 37.5%
Page : 165 , Block Name : Exercise 8.2
Q4 Find:
(a) 15% of 250 (b) 1% of 1 hour (c) 20% of 2500 (d) 75% of 1 kg
15 75
Answer. (a) 15% of 250 = 100 × 250 = 2
= 37.5
(b) 1 hour = 60 minutes
1
1% of 60 minutes = 100 × 60 = 35 minutes
20
(c) 20% of Rs2500 = 100 × 2500 = Rs500
75
(d) 75% of 1kg = 100 × 1 = 0.75kg = (0.75 × 1000)g = 750g
Page 4 of 11 Aglasem Schools
Answer. (i) Here, 1 part out of 4 equal parts are shaded which represents the fraction 14 .
1
4
= 14 × 100% = 25%
(ii) Here, 3 parts out of 5 equal parts are shaded which represents the fraction 35
3
5
= 35 × 100% = 60%
(iii) Here, 3 parts out of 8 equal parts are shaded which represents the fraction 38
3
8
= 38 × 100% = 300
8
% = 37.5%
Page : 165 , Block Name : Exercise 8.2
Q4 Find:
(a) 15% of 250 (b) 1% of 1 hour (c) 20% of 2500 (d) 75% of 1 kg
15 75
Answer. (a) 15% of 250 = 100 × 250 = 2
= 37.5
(b) 1 hour = 60 minutes
1
1% of 60 minutes = 100 × 60 = 35 minutes
20
(c) 20% of Rs2500 = 100 × 2500 = Rs500
75
(d) 75% of 1kg = 100 × 1 = 0.75kg = (0.75 × 1000)g = 750g
Page 4 of 11 Aglasem Schools
Page 6
Book : Mathematics Ncert Solutions | Chapter-8 Maths
Page : 165 , Block Name : Exercise 8.2
Q5 Find the whole quantity if
(a) 5% of it is 600. (b) 12% of it is 1080.
(c) 40% of it is 500 km. (d) 70% of it is 14 minutes. (e) 8% of it is 40 litres.
Answer. (a) 5 % of x = 600
5
100
× x = 600
x = 600 × 100
5
= 12000
(b) 12% of x = Rs1080
12
100
× x = Rs 1080
x = Rs 1080 × 100
12
= Rs 9000
(c) 40 % of x = 500 km
40
100
× x = 500km
x = 500 × 100
40
= 1250km
(d) 70% of x = 14 min.
70
x × 100 = 14 min
x = 14 × 100
70
= 20min
(e) 8% of x =40 L
8
x × 100 = 40L
x = 40 × 100
8
= 500 L
Page : 165 , Block Name : Exercise 8.2
Q6 Convert given per cents to decimal fractions and also to fractions in simplest forms:
(a) 25% (b) 150% (c) 20% (d) 5%
25
Answer. (a) 25% = 100 = 14 = 0.25
150
(b) 150% = 100 = 1.5 = 32
20
(c) 20% = 100 = 0.2 = 15
5 1
(d) 5% = 100 = 0.05 = 20
Page 5 of 11 Aglasem Schools
Page : 165 , Block Name : Exercise 8.2
Q5 Find the whole quantity if
(a) 5% of it is 600. (b) 12% of it is 1080.
(c) 40% of it is 500 km. (d) 70% of it is 14 minutes. (e) 8% of it is 40 litres.
Answer. (a) 5 % of x = 600
5
100
× x = 600
x = 600 × 100
5
= 12000
(b) 12% of x = Rs1080
12
100
× x = Rs 1080
x = Rs 1080 × 100
12
= Rs 9000
(c) 40 % of x = 500 km
40
100
× x = 500km
x = 500 × 100
40
= 1250km
(d) 70% of x = 14 min.
70
x × 100 = 14 min
x = 14 × 100
70
= 20min
(e) 8% of x =40 L
8
x × 100 = 40L
x = 40 × 100
8
= 500 L
Page : 165 , Block Name : Exercise 8.2
Q6 Convert given per cents to decimal fractions and also to fractions in simplest forms:
(a) 25% (b) 150% (c) 20% (d) 5%
25
Answer. (a) 25% = 100 = 14 = 0.25
150
(b) 150% = 100 = 1.5 = 32
20
(c) 20% = 100 = 0.2 = 15
5 1
(d) 5% = 100 = 0.05 = 20
Page 5 of 11 Aglasem Schools
Page 7
Book : Mathematics Ncert Solutions | Chapter-8 Maths
Page : 165 , Block Name : Exercise 8.2
Q7 In a city, 30% are females, 40% are males and remaining are children. What per cent
are children?
Answer. It is given that 30% are females and 40% are males.
Children = (100 - 30 - 40) % = 30 %
Page : 165 , Block Name : Exercise 8.2
Q8 Out of 15,000 voters in a constituency, 60% voted. Find the percentage of voters who
did not vote. Can you now �nd how many actually did not vote?
Answer. Percentage of voters who voted = 60%
Percentage Of those who did not vote = 100% — 60% = 40%
Number of people who did not vote = 40% of 15000
40
= 100 × 15000 = 6000
Therefore, 6000 people did not vote.
Page : 165 , Block Name : Exercise 8.2
Q9 Meeta saves 4000 from her salary. If this is 10% of her salary. What is her salary?
Answer. Let Meeta's salary be Rs x.
Given that, 10% of x = 400
10
100
× x = 400
x
10
= 400
X = 400 X 10 = RS 4000
Therefore, Meeta's salary is Rs 4000.
Page : 165 , Block Name : Exercise 8.2
Q10 A local cricket team played 20 matches in one season. It won 25% of them. How
many matches did they win?
Answer. Number of games won = 25% of 20
25
= 100 × 20 = 5
Therefore, the team won 5 matches.
Page : 165 , Block Name : Exercise 8.2
Page 6 of 11 Aglasem Schools
Page : 165 , Block Name : Exercise 8.2
Q7 In a city, 30% are females, 40% are males and remaining are children. What per cent
are children?
Answer. It is given that 30% are females and 40% are males.
Children = (100 - 30 - 40) % = 30 %
Page : 165 , Block Name : Exercise 8.2
Q8 Out of 15,000 voters in a constituency, 60% voted. Find the percentage of voters who
did not vote. Can you now �nd how many actually did not vote?
Answer. Percentage of voters who voted = 60%
Percentage Of those who did not vote = 100% — 60% = 40%
Number of people who did not vote = 40% of 15000
40
= 100 × 15000 = 6000
Therefore, 6000 people did not vote.
Page : 165 , Block Name : Exercise 8.2
Q9 Meeta saves 4000 from her salary. If this is 10% of her salary. What is her salary?
Answer. Let Meeta's salary be Rs x.
Given that, 10% of x = 400
10
100
× x = 400
x
10
= 400
X = 400 X 10 = RS 4000
Therefore, Meeta's salary is Rs 4000.
Page : 165 , Block Name : Exercise 8.2
Q10 A local cricket team played 20 matches in one season. It won 25% of them. How
many matches did they win?
Answer. Number of games won = 25% of 20
25
= 100 × 20 = 5
Therefore, the team won 5 matches.
Page : 165 , Block Name : Exercise 8.2
Page 6 of 11 Aglasem Schools
Page 8
Book : Mathematics Ncert Solutions | Chapter-8 Maths
Exercise 8.3
Q1 Tell what is the pro�t or loss in the following transactions. Also �nd pro�t per cent or
loss per cent in each case.
(a) Gardening shears bought for Rs.250 and sold for Rs.325.
(b) A refrigerator bought for Rs. 12,000 and sold at Rs. 13,500.
(c) A cupboard bought for Rs. 2,500 and sold at Rs. 3,000.
(d) A skirt bought for Rs.250 and sold at Rs.150.
Answer. (a) cost price = Rs 250
Selling price = RS 325
Pro�t = 325 - 250 = RS 75
Profit % = Profit
CP
× 100
= 30%
75
= 250 × 100
(b) cost price = RS 12000
Selling price = Rs 13,500
Pro�t = 13500 - 12000 = RS 1500
Profit
Profit % = × 100
CP = 12.5%
1500
× 100
12000
(c) cost price = RS 2500
selling price = RS 3000
Pro�t = 3000 - 2500 = Rs 500
Profit
Profit % = × 100
CP = 20%
500
× 100
2500
(d) cost price = RS 250
Selling price = RS 150
Loss = 250 — 150 = RS 100
Los s
Loss % = × 100
CP = 40%
100
× 100
250
Page 7 of 11 Aglasem Schools
Exercise 8.3
Q1 Tell what is the pro�t or loss in the following transactions. Also �nd pro�t per cent or
loss per cent in each case.
(a) Gardening shears bought for Rs.250 and sold for Rs.325.
(b) A refrigerator bought for Rs. 12,000 and sold at Rs. 13,500.
(c) A cupboard bought for Rs. 2,500 and sold at Rs. 3,000.
(d) A skirt bought for Rs.250 and sold at Rs.150.
Answer. (a) cost price = Rs 250
Selling price = RS 325
Pro�t = 325 - 250 = RS 75
Profit % = Profit
CP
× 100
= 30%
75
= 250 × 100
(b) cost price = RS 12000
Selling price = Rs 13,500
Pro�t = 13500 - 12000 = RS 1500
Profit
Profit % = × 100
CP = 12.5%
1500
× 100
12000
(c) cost price = RS 2500
selling price = RS 3000
Pro�t = 3000 - 2500 = Rs 500
Profit
Profit % = × 100
CP = 20%
500
× 100
2500
(d) cost price = RS 250
Selling price = RS 150
Loss = 250 — 150 = RS 100
Los s
Loss % = × 100
CP = 40%
100
× 100
250
Page 7 of 11 Aglasem Schools
Page 9
Book : Mathematics Ncert Solutions | Chapter-8 Maths
Page : 171 , Block Name : Exercise 8.3
Q2 Convert each part of the ratio to percentage:
(a) 3 : 1 (b) 2 : 3 : 5 (c) 1:4 (d) 1 : 2 : 5
Answer. (a) 3:1
Total parts = 3 + 1 = 4
1st part = 34 = 34 × 100% = 75%
2 nd part = 14 = 14 × 100% = 25%
(b) 2 : 3 : 5
Total Parts = 2 + 3 + 5 = 10
2 2
1st part = 10 = 10 × 100% = 20%
3 3
2 nd part = 10 = 10 × 100% = 30%
5 5
3rd part = 10 = 10 × 100% = 50%
(c) 1:4
Total Parts = 1 + 4 = 5
1st part = 15 = 15 × 100% = 20%
2 nd part = 45 = 45 × 100% = 80%
(d) 1:2:5
Total Parts = 1 + 2 + 5 = 8
1st part = 18 = 18 × 100% = 12.5%
2 nd part = 28 = 28 × 100% = 25%
3rd part = 58 = 58 × 100% = 62.5%
Page : 171 , Block Name : Exercise 8.3
Q3 The population of a city decreased from 25,000 to 24,500. Find the percentage
decrease.
Answer. Initial population = 25000
Final population = 24500
Decrease = 500
500
% decrease = 25000 × 100 = 2%
Page : 171 , Block Name : Exercise 8.3
Page 8 of 11 Aglasem Schools
Page : 171 , Block Name : Exercise 8.3
Q2 Convert each part of the ratio to percentage:
(a) 3 : 1 (b) 2 : 3 : 5 (c) 1:4 (d) 1 : 2 : 5
Answer. (a) 3:1
Total parts = 3 + 1 = 4
1st part = 34 = 34 × 100% = 75%
2 nd part = 14 = 14 × 100% = 25%
(b) 2 : 3 : 5
Total Parts = 2 + 3 + 5 = 10
2 2
1st part = 10 = 10 × 100% = 20%
3 3
2 nd part = 10 = 10 × 100% = 30%
5 5
3rd part = 10 = 10 × 100% = 50%
(c) 1:4
Total Parts = 1 + 4 = 5
1st part = 15 = 15 × 100% = 20%
2 nd part = 45 = 45 × 100% = 80%
(d) 1:2:5
Total Parts = 1 + 2 + 5 = 8
1st part = 18 = 18 × 100% = 12.5%
2 nd part = 28 = 28 × 100% = 25%
3rd part = 58 = 58 × 100% = 62.5%
Page : 171 , Block Name : Exercise 8.3
Q3 The population of a city decreased from 25,000 to 24,500. Find the percentage
decrease.
Answer. Initial population = 25000
Final population = 24500
Decrease = 500
500
% decrease = 25000 × 100 = 2%
Page : 171 , Block Name : Exercise 8.3
Page 8 of 11 Aglasem Schools
Page 10
Book : Mathematics Ncert Solutions | Chapter-8 Maths
Q4 Arun bought a car for Rs. 3,50,000. The next year, the price went upto Rs. 3,70,000.
What was the Percentage of price increase?
Answer. Initial price = RS 350000
Final price = RS 370000
Increase = Rs 20000
20000 5
% increase = 350000 × 100 = 5 7 %
Page : 171 , Block Name : Exercise 8.3
Q5 I buy a T.V. for Rs.10,000 and sell it at a pro�t of 20%. How much money do I get for
it?
Answer. C.P. = 10000
Pro�t = 20% of C.P.
= 20% of 10000
20
= 100 × 10, 000
= 2000
∴ S. P = C. P+ Pro�t
= 10000 + 2000
= 12000, Hence I get 12000 for it.
Page : 171 , Block Name : Exercise 8.3
Q6 Juhi sells a washing machine for Rs. 13,500. She loses 20% in the bargain. What was
the price at which she bought it?
Answer. Selling price = Rs 13500
LOSS % = 20%
Let the cost price be x.
∴ LOSS = 20% of x
Cost price — Loss = Selling price
20
x − 100 × x = 13500
x − 15 x = 13500
= 16875
4
5
x = 13500
x = 13500 × 54
Therefore, she bought it for Rs 16875.
Page : 171 , Block Name : Exercise 8.3
Page 9 of 11 Aglasem Schools
Q4 Arun bought a car for Rs. 3,50,000. The next year, the price went upto Rs. 3,70,000.
What was the Percentage of price increase?
Answer. Initial price = RS 350000
Final price = RS 370000
Increase = Rs 20000
20000 5
% increase = 350000 × 100 = 5 7 %
Page : 171 , Block Name : Exercise 8.3
Q5 I buy a T.V. for Rs.10,000 and sell it at a pro�t of 20%. How much money do I get for
it?
Answer. C.P. = 10000
Pro�t = 20% of C.P.
= 20% of 10000
20
= 100 × 10, 000
= 2000
∴ S. P = C. P+ Pro�t
= 10000 + 2000
= 12000, Hence I get 12000 for it.
Page : 171 , Block Name : Exercise 8.3
Q6 Juhi sells a washing machine for Rs. 13,500. She loses 20% in the bargain. What was
the price at which she bought it?
Answer. Selling price = Rs 13500
LOSS % = 20%
Let the cost price be x.
∴ LOSS = 20% of x
Cost price — Loss = Selling price
20
x − 100 × x = 13500
x − 15 x = 13500
= 16875
4
5
x = 13500
x = 13500 × 54
Therefore, she bought it for Rs 16875.
Page : 171 , Block Name : Exercise 8.3
Page 9 of 11 Aglasem Schools
Page 11
Book : Mathematics Ncert Solutions | Chapter-8 Maths
Q7 (i) Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the
percentage of carbon in chalk.
(ii) If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick?
Answer. (i) Ratio of calcium, carbon, and oxygen = 10:3:12
As 10 + 3 +12 = 25,
3
Therefore, percentage of Carbon = 25 × 100 = 12%
(ii) Let the weight of the stick be x g.
12% of x = 3
12
100
×x=3
x = 3 × 100
12
= 25g
Page : 171 , Block Name : Exercise 8.3
Q8 Amina buys a book for Rs. 275 and sells it at a loss of 15%. How much does she sell it
for?
Answer. Cost price = Rs 275
LOSS % = 15%
LOSS = 15% of 275
Cost price — Loss = Selling price
15
275 − 100 × 275 = Selling price
275 − 4125
100
= Selling price
275 - 41.25 = Selling Price
Selling Price = Rs 233.75
Page : 172 , Block Name : Exercise 8.3
Q9 Find the amount to be paid at the end of 3 years in each case:
(a) Principal = Rs. 1,200 at 12% p.a. (b) Principal = Rs. 7,500 at 5% p.a.
Answer. (a) Principal (P) = Rs. 1,200
Rate (R) = 12% p.a.
Time (T) = 3 years
P×R×T
S.I =
100
1200 × 12 × 3
=
100
Page 10 of 11 Aglasem Schools
Q7 (i) Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the
percentage of carbon in chalk.
(ii) If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick?
Answer. (i) Ratio of calcium, carbon, and oxygen = 10:3:12
As 10 + 3 +12 = 25,
3
Therefore, percentage of Carbon = 25 × 100 = 12%
(ii) Let the weight of the stick be x g.
12% of x = 3
12
100
×x=3
x = 3 × 100
12
= 25g
Page : 171 , Block Name : Exercise 8.3
Q8 Amina buys a book for Rs. 275 and sells it at a loss of 15%. How much does she sell it
for?
Answer. Cost price = Rs 275
LOSS % = 15%
LOSS = 15% of 275
Cost price — Loss = Selling price
15
275 − 100 × 275 = Selling price
275 − 4125
100
= Selling price
275 - 41.25 = Selling Price
Selling Price = Rs 233.75
Page : 172 , Block Name : Exercise 8.3
Q9 Find the amount to be paid at the end of 3 years in each case:
(a) Principal = Rs. 1,200 at 12% p.a. (b) Principal = Rs. 7,500 at 5% p.a.
Answer. (a) Principal (P) = Rs. 1,200
Rate (R) = 12% p.a.
Time (T) = 3 years
P×R×T
S.I =
100
1200 × 12 × 3
=
100
Page 10 of 11 Aglasem Schools
Page 12
Book : Mathematics Ncert Solutions | Chapter-8 Maths
= Rs 432
Amount = P + SI
= 1200 + 432 = Rs 1632
(b) P = RS 7500
R = 5% p.a.
T = 3 years
P×R×T
S.I. =
100 = Rs. 1125
7500 × 5 × 3
=
100
Amount = 7500 + 1125
= Rs. 8625
Page : 172 , Block Name : Exercise 8.3
Q10 What rate gives Rs. 280 as interest on a sum of Rs.56,000 in 2 years?
S. I = P×R×T
100
Answer. 280 = 56000×R×2
100
280
R = 560×2 = 14 = 0.25
Therefore, 0.25% gives Rs 280 as interest on the given sum.
Page : 172 , Block Name : Exercise 8.3
Q11 If Meena gives an interest of 45 for one year at 9% rate p.a.. What is the sum she has
borrowed?
S. I = P×R×T
100
P×9×1
Answer. 45 = 100
45×100
P= 9
= Rs 500
Therefore, she borrowed Rs 500.
Page : 172 , Block Name : Exercise 8.3
Page 11 of 11 Aglasem Schools
= Rs 432
Amount = P + SI
= 1200 + 432 = Rs 1632
(b) P = RS 7500
R = 5% p.a.
T = 3 years
P×R×T
S.I. =
100 = Rs. 1125
7500 × 5 × 3
=
100
Amount = 7500 + 1125
= Rs. 8625
Page : 172 , Block Name : Exercise 8.3
Q10 What rate gives Rs. 280 as interest on a sum of Rs.56,000 in 2 years?
S. I = P×R×T
100
Answer. 280 = 56000×R×2
100
280
R = 560×2 = 14 = 0.25
Therefore, 0.25% gives Rs 280 as interest on the given sum.
Page : 172 , Block Name : Exercise 8.3
Q11 If Meena gives an interest of 45 for one year at 9% rate p.a.. What is the sum she has
borrowed?
S. I = P×R×T
100
P×9×1
Answer. 45 = 100
45×100
P= 9
= Rs 500
Therefore, she borrowed Rs 500.
Page : 172 , Block Name : Exercise 8.3
Page 11 of 11 Aglasem Schools
Document Details
| Board / Org | NCERT |
| Exam | Class 7 |
| Type | Solution |
| Pages | 12 |
| Updated | 30 Apr 2026 |