NCERT Solutions for Class 7 Maths Exercise 8.2 Chapter 8 Comparing Quantities in simple PDF are given here. Comparing Quantities solutions are extremely helpful for the students to clear all their doubts easily and understand the basics of this chapter more effectively. Percentage-another way of comparing quantities, converting fractional numbers to percentage, converting decimals to percentage and converting percentage to fraction or decimals are the key topics covered in this exercise. Students of Class 7 are suggested to solve NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities to strengthen the fundamentals and be able to solve questions that are usually asked in the examination.

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**1. Convert the given fractional numbers to percent.**

**(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:-**

= (2/7) × 100 %

= 200/7 %

=

%

**2. Convert the given decimal fraction to percent.**

**(a) 0.65**

**Solution:-**

First we have to remove the decimal point,

= 65/100

Now,

Multiply by 100 and put the percent sign %.

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 sign %.

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 sign %.

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 sign %.

We have,

= (1235/100) × 100)

= 1235%

**3. Estimate what part of the figures is coloured and hence find the per cent 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 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 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 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 percent to decimal fractions and also fractions in simplest forms:**

**(a) 25%**

**Solution:-**

First convert the given percentage into fraction and then put the fraction into decimal form.

= (25/100)

= ¼

= 0.25

**(b) 150%**

**Solution:-**

First convert the given percentage into fraction and then put the fraction into decimal form.

= (150/100)

= 3/2

= 1.5

**(c) 20%**

**Solution:-**

First convert the given percentage into fraction and then put the fraction into decimal form.

= (20/100)

= 1/5

= 0.2

**(d) 5%**

**Solution:-**

First convert the given percentage into 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 remaining are children. What per cent are children?**

**Solution:-**

From the question, it is given that

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:-**

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 voted in the election = 100 – 60

= 40%

Total number of voters who did not voted 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.

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