Mathematics – Class 7 – Chapter 8 – Comparing Quantities – Exercise 8.2 – NCERT Exercise Solution

1. Convert the given fractional numbers to percent.

Note: To convert a fraction into a percentage we have to multiply the fraction by 100 and put the percent sign %.

(a) 1/8

Solution:

= (1/8) × 100 %

= 100/8 %

= 12.5%

(b) 5/4

Solution:

= (5/4) × 100 %

= 500/4 %

= 125%

(c) 3/40

Solution:

= (3/40) × 100 %

= 300/40 %

= 30/4 %

= 7.5%

(d) 2/7

Solution:

= (2/7) × 100 %

= 200/7 %

= 28.57 %

2. Convert the given decimal fraction to percent.

(a) 0.65

Solution:

First, remove the decimal point,

= 65/100

Now,

Multiply the fraction by 100 and put the percent sign %.

= (65/100) × 100

= 65%

(b) 2.1

Solution:

First, remove the decimal point,

= 21/10

Now,

Multiply the fraction by 100 and put the percent sign %.

= (21/10) × 100

=210%

(c) 0.02

Solution:

First, remove the decimal point,

= 2/100

Now,

Multiply the fraction by 100 and put the percent sign %.

= (2/100) × 100

= 2%

(d) 12.35

Solution:

First, remove the decimal point,

= 1235/100

Now,

Multiply the fraction by 100 and put the percent sign %.

= (1235/100) × 100) = 1235%

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

(i)

Mathematics - Class 7 - Chapter 8 - Comparing Quantities - Exercise 8.2 - NCERT Exercise Solution

Solution:

After observing the given figure, we are now able to identify that 1 part is shaded out of 4 equal parts.

So,

It is represented by a fraction = 1/4

Now,

= (1/4) × 100

= 100/4

= 25%

Hence, 25% of figure is coloured.

(ii)

Mathematics - Class 7 - Chapter 8 - Comparing Quantities - Exercise 8.2 - NCERT Exercise Solution

Solution:

After observing the given figure, we are now able to identify that the 3 part is shaded out of 5 equal parts.

So,

It is represented by a fraction = 3/5

Now,

= (3/5) × 100

= 300/5

= 60%

Hence, 60% of figure is coloured.

(iii)

Mathematics - Class 7 - Chapter 8 - Comparing Quantities - Exercise 8.2 - NCERT Exercise Solution

Solution:

After observing the given figure, we are now able to identify that the 3 part is shaded out of 8 equal parts.

So,

It is represented by a fraction = 3/8

Now,

= (3/8) × 100

= 300/8

= 37.5%

Hence, 37.5% of figure is coloured.

4. Find:

(a) 15% of 250

Solution:

According to question:

= (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,

According to the question we have to find,

1% of 60 minutes

1 minute = 60 seconds

60 minutes = 60 × 60 = 3600 seconds

Now,

According to the question we have to find,

1% of 3600 seconds

= (1/100) × 3600

= 1 × 36

= 36 seconds

(c) 20% of ₹ 2500

Solution:

According to question,

= (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 the whole quantity to be x,

Then,

According to question,

(5/100) × (x) = 600

X = 600 × (100/5)

X = 60000/5

X = 12000

Hence the whole quantity is 12000.

(b) 12% of it is ₹ 1080.

Solution:

Let the whole quantity be x,

Then,

According to question,

(12/100) × (x) = 1080

X = 1080 × (100/12)

X = 540 × (100/6)

X = 90 × 100

X = ₹ 9000

Hence the whole quantity is ₹ 9000

(c) 40% of it is 500 km

Solution:

Let the whole quantity be x,

Then,

According to question,

(40/100) × (x) = 500

X = 500 × (100/40)

X = 500 × (10/4)

X = 500 × 2.5

X = 1250 km

Hence the whole quantity is 1250 km

(d) 70% of it is 14 minutes

Solution:

Let the whole quantity be x,

Then,

According to question,

(70/100) × (x) = 14

X = 14 × (100/70)

X = 14 × (10/7)

X = 20 minutes

(e) 8% of it is 40 liters

Solution:

Let the whole quantity be x,

Then,

According to question,

(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,

= (25/100)

= 1/4

Now, put the fraction into decimal form,

= 0.25

(b) 150%

Solution:

First, convert the given percentage into a fraction

= (150/100)

= 3/2

Now, put the fraction into decimal form

= 1.5

(c) 20%

Solution:

First, convert the given percentage into fraction,

= (20/100)

= 1/5

Now, put the fraction into decimal form

= 0.2

(d) 5%

Solution:

First, convert the given percentage into fraction,

= (5/100)

= 1/20

Now, put the fraction into decimal form

= 0.05

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

Solution:

Given,

Percentage of female in a city =30%

Percentage of male in a city = 40%

Then, total percentage of male and female both = 40% + 30%

                                                                                      = 70%

Total percentage of people (male + female + children) = 100

Now, the percentage of children = 100 – 70

                                                          = 30%

Hence, percentage of children is 30%.

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:

Given,

Total number of voters in the constituency = 15000

Total percentage of people who voted in the election = 60%

Let the total percentage of people = 100%

Then, the Total percentage of people who did not vote in the election = 100 – 60

                                                                                                                        = 40%

Now,

Total number of voters who did not voted in the election = 40% of 15000

= (40/100) × 15000

= 0.4 × 15000

= 6000 voters

Hence, 6000 voters did not vote.

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

Solution:

Given, 10 % of Meeta’s salary = ₹ 4000

Let the salary of  Meeta is ₹ x,

Then,

According to question,

10% of ₹ x = ₹ 4000

(10/100) × (x) = 4000

X = 4000 × (100/10)

X = 4000 × 10

X = ₹ 40000

Hence, 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:

Given,

Total matches played by a local team = 20

Percentage of matches won by the local team = 25%

According to the question,

Number of matches won by the team = 25% of 20

= (25/100) × 20

= 25/5

= 5 matches.

Hence, The local team won 5 matches out of 20 matches.

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