NCERT Solutions Class 7 Math Chapter – 7 Comparing Quantities Exercise 7.1

1. Convert the given fractional numbers to per cent.

(a) 1/8

Solution: In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.
= (1/8) × 100 %
= 100/8 %
= 12.5%

(b) 5/4

Solution:  In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.
= (5/4) × 100 %
= 500/4 %
= 125%

(c) 3/40

Solution: In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.
= (3/40) × 100 %
= 300/40 %
= 30/4 %
= 7.5%

(d) 2/7

Solution: In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.
= (2/7) × 100 %
= 200/7 %
= 28 4/7%

2. Convert the given decimal fraction to per cent.

(a) 0.65

Solution: First we have to remove the decimal point,
= 65/100
Now,
Multiply by 100 and put the percent  %.
We have,
= (65/100) × 100
= 65%

(b) 2.1

Solution: First we have to remove the decimal point,
= 21/10
Now,
Multiply by 100 and put the percent  %.
We have,
= (21/10) × 100
=210%

(c) 0.02

Solution: First we have to remove the decimal point,
= 2/100
Now,
Multiply 100 and put the percent  %.
We have,
= (2/100) × 100
= 2%

(d) 12.35

Solution: First we have to remove the decimal point,
= 1235/100
Now,
Multiply by 100 and put the percent  %.
We have,
= (1235/100) × 100)
= 1235%

3. Estimate what part of the figures is coloured and hence find the percent which is coloured.

(i)

Solution: By observing the given figure,
We can able to identify that 1 part is shaded out of 4 equal parts.
It is represented by a fraction = ¼
Then,
= ¼ × 100
= 100/4
= 25%
Hence, 25% of the figure is coloured.

(ii)

Solution: By observing the given figure,
We can able to identify that 3 part is shaded out of 5 equal parts.
It is represented by a fraction = 3/5
Then,
= (3/5) × 100
= 300/5
= 60%
Hence, 60% of the figure is coloured.

(iii)

Solution: By observing the given figure,
We can able to identify that 3 part is shaded out of 8 equal parts.
It is represented by a fraction = 3/8
Then,
= (3/8) × 100
= 300/8
= 37.5%
Hence, 37.5% of the figure is coloured.

4. Find:

(a) 15% of 250

Solution: We have,
= (15/100) × 250
= (15/10) × 25
= (15/2) × 5
= (75/2)
= 37.5

(b) 1% of 1 hour

Solution: We know that,
1 hour = 60 minutes
Then,
1% of 60 minutes
1 minute = 60 seconds
60 minutes = 60 × 60 = 3600 seconds
Now,
1% of 3600 seconds
= (1/100) × 3600
= 1 × 36
= 36 seconds

(c) 20% of ₹ 2500

Solution: We have,
= (20/100) × 2500
= 20 × 25
= ₹ 500

(d) 75% of 1 kg

Solution: We know that, 1 kg = 1000 g
Then,
75% of 1000 g
= (75/100) × 1000
= 75 × 10
= 750 g

5. Find the whole quantity if

(a) 5% of it is 600

Solution: Let us assume the whole quantity be x,
Then, (5/100) × (x) = 600
X = 600 × (100/5)
X = 60000/5
X = 12000

(b) 12% of it is ₹ 1080.

Solution: Let us assume the whole quantity be x,
Then,
(12/100) × (x) = 1080
X = 1080 × (100/12)
X = 540 × (100/6)
X = 90 × 100
X = ₹ 9000

(c) 40% of it is 500k km

Solution:  Let us assume the whole quantity be x,
Then,
(40/100) × (x) = 500
X = 500 × (100/40)
X = 500 × (10/4)
X = 500 × 2.5
X = 1250 km

(d) 70% of it is 14 minutes

Solution: Let us assume the whole quantity be x,
Then,
(70/100) × (x) = 14
X = 14 × (100/70)
X = 14 × (10/7)
X = 20 minutes

(e) 8% of it is 40 liters

Solution: Let us assume the whole quantity be x,
Then,
(8/100) × (x) = 40
X = 40 × (100/8)
X = 40 × (100/8)
X = 40 × 12.5
X = 500 liters

6. Convert given per cent to decimal fractions and also fractions in simplest forms:

(a) 25%

Solution: First convert the given percentage into a fraction and then put the fraction into decimal form.
= (25/100)
= ¼
= 0.25

(b) 150%

Solution: First convert the given percentage into a fraction and then put the fraction into decimal form.
= (150/100)
= 3/2
= 1.5

(c) 20%

Solution: First convert the given percentage into a fraction and then put the fraction into decimal form.
= (20/100)
= 1/5
= 0.2

(d) 5%

Solution: First convert the given percentage into a fraction and then put the fraction into decimal form.
= (5/100)
= 1/20
= 0.05

7. In a city, 30% are females, 40% are males and the remaining are children. What per cent are children?

Solution: From the question, it is given that
Percentage of females in a city =30%
Percentage of males in a city = 40%
Total percentage of male and female both = 40% + 30%
= 70%
Now we have to find the percentage of children = 100 – 70
= 30%
So, 30% are children.

8. Out of 15,000 voters in a constituency, 60% voted. Find the percentage of voters who did not vote. Can you now find how many actually did not vote?

Solution: From the question, it is given that
Total number of voters in the constituency = 15000
Percentage of people who voted in the election = 60%
Percentage of people who did not vote in the election = 100 – 60
= 40%
Total number of voters who did not vote in the election = 40% of 15000
= (40/100) × 15000
= 0.4 × 15000
= 6000 voters
∴ 6000 voters did not vote.

9. Meeta saves ₹ 4000 from her salary. If this is 10% of her salary. What is her salary?

Solution: Let us assume Meeta’s salary be ₹ x,
Then,
10% of ₹ x = ₹ 4000
(10/100) × (x) = 4000
X = 4000 × (100/10)
X = 4000 × 10
X = ₹ 40000
∴ Meeta’s salary is ₹ 40000.

10. A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?

Solution: From the question, it is given that
Total matches played by a local team = 20
Percentage of matches won by the local team = 25%
Then,
Number of matches won by the team = 25% of 20
= (25/100) × 20
= 25/5
= 5 matches.
∴The local team won 5 matches out of 20 matches.