Class 7 Comparing Quantities Ex 7.1

Question 1. Convert the given fractional numbers to percent.(a) \(\dfrac{1}{8}\)

Solution:-

\(\dfrac{1}{8}\) × 100 %

= 12.5%

(b) \(\dfrac{5}{4}\)

Solution:-

= \(\dfrac{5}{4}\) × 100 %

= 125%

(c) \(\dfrac{3}{40}\)

Solution:-

= \(\dfrac{3}{40}\) × 100 %

= \(\dfrac{15}{2}\) %

= 7.5%

(d) \(2\over7\)

Solution:-

\(\dfrac{2}{7}\) × 100 %

= \(\dfrac{200}{7}\) %

=28\(\dfrac{4}{7}\) %

Question 2. Convert the given decimal fraction to percent.

(a) 0.65

Solution:-

0.65= \(\dfrac{65}{100}\)

Multiply by 100 and put the percent sign %

= \(\dfrac{65}{100}\) × 100

= 65%

(b) 2.1

Solution:-

2.1= \(\dfrac{21}{10}\)

Multiply by 100 and put the percent sign %.

= \(\dfrac{21}{10}\) × 100

=210%

(c) 0.02

Solution:-

0.02 = \(\dfrac{2}{100}\)

Multiply 100 and put the percent sign %.

= \(\dfrac{2}{100}\) × 100

= 2%

(d) 12.35

Solution:-

12.35 = \(\dfrac{1235}{100}\)

Multiply by 100 and put the percent sign %.

= \(\dfrac{1235}{100}\) × 100

= 1235%

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

Solution:-

(i) It is represented by a fraction = \(1 \over 4\)

= \(\dfrac{1 }{ 4}\) × 100

= 25%

Hence, 25% of figure is colored.

(ii) We can able to identify that 3 part is shaded out of 5 equal parts.

It is represented by a fraction = \(\dfrac{3}{5}\)

= \(\dfrac{3}{5}\) × 100

= \(\dfrac{300}{5}\)

= 60%

Hence, 60% of figure is colored.


(iii)We can able to identify that 3 part is shaded out of 8 equal parts.

It is represented by a fraction =\( 3\over8\)


= \( \dfrac{3}{8}\) × 100

= \(\dfrac{300}{ 8}\)

= 37.5%

Hence, 37.5% of figure is colored.

Question 4. Find:

(a) 15% of 250

Solution:-

= \(\dfrac{15}{100}\) × 250

= \(\dfrac{15}{2}\) × 5

= \(\dfrac{75}{2}\)

= 37.5

(b) 1% of 1 hour

Solution:-

1 hour = 60 minutes

1% of 60 minutes

1 minute = 60 seconds

60 minutes = 60 × 60 = 3600 seconds

1% of 3600 seconds

= \(\dfrac{1}{100}\) × 3600

= 1 × 36

= 36 seconds

(c) 20% of ₹ 2500

Solution:-

= \(\dfrac{20}{100} × 2500\)

= 20 × 25

= ₹ 500

(d) 75% of 1 kg

Solution:-

1 kg = 1000 g

75% of 1000 g

\(= \dfrac{75}{100} × 1000\)

\(= 75 × 10\)

\(= 750\) g

So, 30% are children.

Question 5. Find the whole quantity if

(a) 5% of it is 600

Solution:-

Let the whole quantity be \(x\),

\(\dfrac{5}{100}\) × x = 600

\(x = \dfrac{600 × 100}{5}\)

\(x = \dfrac{60000}{5}\)

\(x = 12000\)

(b) 12% of it is ₹ 1080.

Solution:-

Let us assume the whole quantity be \(x\),

\(\dfrac{12}{100} × x = 1080\)

\(x = 1080 × \dfrac{100}{12}\)

\(x = 540 ×\dfrac{100}{6}\)

\(x = 90 × 100\)

x = ₹ 9000

(c) 40% of it is 500 km

Solution:-

Let the whole quantity be \(x\),

\(\dfrac{40}{100} × x = 500\)

x = 500 × \(\dfrac{100}{40}\)

x = 500 × \(\dfrac{10}{4}\)

x = 500 × 2.5

x = 1250 km

(d) 70% of it is 14 minutes

Solution:-

Let the whole quantity be \(x\),

\(\dfrac{70}{100}\) × x = 14

x = 14 × \(\dfrac{100}{70}\)

x = 14 × \(\dfrac{10}{7}\)

x = 20 minutes

(e) 8% of it is 40 liters

Solution:-

Let the whole quantity be x,

\(\dfrac{8}{100} × x = 40\)

x = 40 × \(\dfrac{100}{8}\)

x = 40 × 12.5

x = 500 liters

Question 6. Convert given percent to decimal fractions and also fractions in simplest forms:

(a) 25%

Solution:-

= \(\dfrac{25}{100}\)

= \(\dfrac{1}{4}\)

= 0.25

(b) 150%

Solution:-

= \(\dfrac{150}{100}\)

= \(\dfrac{3}{2}\)

= \(1.5\)

(c) 20%

Solution:-

= \(\dfrac{20}{100}\)

= \(\dfrac{1}{5}\)

= 0.2

(d) \(5\)%

Solution:-

= \(\dfrac{5}{100}\)

= \(\dfrac{1}{20}\)

=\( 0.05\)

Question 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%

Question 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 \(15000\)

= \(\dfrac{40}{100} × 15000\)

= 0.4 × 15000

= 6000 voters

∴ 6000 voters did not vote.

Question 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 ₹ \(x\),

10% of ₹ x = ₹ 4000

\(\dfrac{10}{100} × x = 4000\)

\(x = 4000 × \dfrac{100}{10}\)

x = 4000 × 10

x = ₹ 40000

∴ Meeta’s salary is ₹ 40000.

Question 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%

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

= \(\dfrac{25}{100} × 20\)

= \(\dfrac{25}{5}= 5 \text{ matches} \)

∴The local team won 5 matches out of 20 matches.