NCERT Solutions Class 7 Mathematics
Chapter – 8 (Comparing Quantities)
The NCERT Solutions in English Language for Class 7 Mathematics Chapter – 8 Comparing Quantities Exercise 8.2 has been provided here to help the students in solving the questions from this exercise.
Chapter : 8 Comparing Quantities
Exercise – 8.2
1. Convert the given fractional numbers to percent.
(a)
Solution –
(a)
In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.
⇒
⇒
(b)
In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.
⇒
⇒ 5 × 25 %
⇒ 125%
(c)
In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.
⇒
⇒
⇒
(d)
In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.
⇒
⇒
2. Convert the given decimal fraction to percent.
(a) 0.65 (b) 2.1 (c) 0.02 (d) 12.35
Solution –
(a) 0.65
First we have to remove the decimal point,
=
Now,
Multiply by 100 and put the percent sign %.
We have,
=
= 65%
(b) 2.1
First we have to remove the decimal point,
=
Now,
Multiply by 100 and put the percent sign %.
We have,
=
= 210%
(c) 0.02
First we have to remove the decimal point,
=
Now,
Multiply 100 and put the percent sign %.
We have,
=
= 2%
(d) 12.35
First we have to remove the decimal point,
=
Now,
Multiply by 100 and put the percent sign %.
We have,
=
= 1235%
3. Estimate what part of the figures is coloured and hence find the per cent which is coloured.
Solution –
(i) Fraction of coloured part =
∴ Percentage of coloured parts 100
=
(ii) Fraction of coloured part =
∴ Percentage of coloured parts
=
= 3 × 20%
= 60%
(iii) Fraction of coloured part =
∴ Percentage of coloured parts
=
=
= 37.5%
4. Find:
(a) 15% of 250
(b) 1% of 1 hour
(c) 20% of ₹ 2500
(d) 75% of 1 kg
Solution –
(a) 15% of 250
We have,
=
=
=
= 37.5
(b) 1% of 1 hour
We know that, 1 hour = 60 minutes
Then,
1% of 60 minutes
1 minute = 60 seconds
60 minutes = 60 × 60 = 3600 seconds
1% of 3600 seconds
=
= 1 × 36
= 36 seconds
(c) 20% of ₹ 2500
=
= 20 × 25
= ₹ 500
(d) 75% of 1 kg
We know that, 1 kg = 1000 g
Then,
75% of 1000 g
=
= 75 × 10
= 750 g
5. 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
Solution –
(a) 5% of it is 600
Let us assume the whole quantity be x,
Then,
x = 600 ×
x = 600 × 20
x = 12000
(b) 12% of it is ₹ 1080.
Let us assume the whole quantity be x,
Then,
x = 1080 ×
x = 90 × 100
x = ₹ 9000
(c) 40% of it is 500k km
Let us assume the whole quantity be x,
Then,
x = 500 ×
x = 500 ×
x = 500 × 2.5
x = 1250 km
(d) 70% of it is 14 minutes
Let us assume the whole quantity be x,
Then,
x = 14 ×
x = 2 × 10
x = 20 minutes
(e) 8% of it is 40 liters
Let us assume the whole quantity be x,
Then,
x = 40 ×
x = 5 × 100
x = 500 liters
6. Convert given percent to decimal fractions and also fractions in simplest forms:
(a) 25%
(b) 150%
(c) 20%
(d) 5%
Solution –
(a) 25%
First convert the given percentage into fraction and then put the fraction into decimal form.
=
= ¼
= 0.25
(b) 150%
First convert the given percentage into fraction and then put the fraction into decimal form.
=
=
= 1.5
(c) 20%
First convert the given percentage into fraction and then put the fraction into decimal form.
=
=
= 0.2
(d) 5%
First convert the given percentage into fraction and then put the fraction into decimal form.
=
=
= 0.05
7. In a city, 30% are females, 40% are males and remaining are children. What per cent are children?
Solution –
Percentage of female in a city =30%
Percentage of male 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 –
Total number of voters in the constituency = 15000
Percentage of people who voted in the election = 60%
Percentage of people who did not voted in the election = 100 – 60
= 40%
Total number of voters who did not voted in the election = 40% of 15000
=
= 40 × 150
= 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
x = 4000 ×
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 –
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
=
=
= 5 matches.
∴ The local team won 5 matches out of 20 matches.