NCERT Solutions for Class 7 Maths Chapter 7 - Comparing Quantities Exercise 7.1

Exercise 7.1

1. Convert the given fractional numbers to percent: 

(a) $\frac{\text{1}}{\text{8}}$

Ans: A fractional number is given, $\frac{1}{8}$

$\frac{1}{8} =\frac{1}{8} \times 100 \%$

$=\frac{25}{2} \%=12.5 \%$

$\Rightarrow  \frac{1}{8}=12.5 \%$

(b) $\frac{\text{5}}{\text{4}}$

Ans: A fractional number is given, $\frac{\text{5}}{\text{4}}$

$\frac{5}{4}=\frac{5}{4} \times 100 \%$

$=5 \times 25 \%$

$=125 \%$

$\Rightarrow  \frac{5}{4}=125 \%$

(c) $\frac{\text{3}}{\text{40}}$

Ans: A fractional number is given, $\frac{\text{3}}{\text{40}}$

$\frac{3}{40}=\frac{3}{40} \times 100 \%$

$\quad=\frac{15}{2} \%$

$=7.5 \%$

$\Rightarrow \frac{3}{40}=7.5 \%$

(d) $\frac{\text{2}}{\text{7}}$

Ans: A fractional number is given, $\frac{\text{2}}{\text{7}}$

$\frac{2}{7}=\frac{2}{7} \times 100 \% $

$=\frac{200}{7} \%$

$=28 \frac{4}{7} \%$

$\Rightarrow  \frac{2}{7}=28 \frac{4}{7} \%$

2. Convert the given decimal fractions to percents:

(a) $\text{0}\text{.65}$

Ans: A decimal fraction is given, needed to convert it into percentage from

$\Rightarrow 0.65=\frac{65}{100}$

$\Rightarrow 0.65=65 \%$

(b) $\text{2}\text{.1}$

Ans: A decimal fraction is given, needed to convert it into percentage from

$\Rightarrow 2.1=\frac{21}{10} \times 100 \%$

$\Rightarrow 2.1=210 \%$

(c) $\text{0}\text{.02}$

Ans: A decimal fraction is given, needed to convert it into percentage from

$\Rightarrow 0.02=\frac{2}{100}$

$\Rightarrow 0.02=2 \%$

(d) $\text{12}\text{.35}$

Ans: A decimal fraction is given, needed to convert it into percentage from

$\Rightarrow 12.35=\frac{1235}{100} \times 100 \%$

$\Rightarrow 12.35=1235 \%$

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

(i)

Ans: It is clear from the figure that the coloured part is $\text{= }\frac{\text{1}}{\text{4}}$

Therefore, the required percentage of coloured parts,

is $=\frac{1}{4} \times \frac{25}{25} $

$=\frac{25}{100} $

$=25 \%$

(ii)

Ans: It is clear from the figure that the coloured part is $\text{= }\frac{\text{3}}{\text{5}}$

Therefore, the required percentage of coloured parts,

 is $\text{= }\frac{\text{3}}{\text{5}}\text{  }\!\!\times\!\!\text{  }\frac{\text{20}}{\text{20}}$

$\text{= }\frac{\text{60}}{\text{100}}$

$\text{= 60 }\%$

(iii)

Ans: It is clear from the figure that the coloured part is $\text{= }\frac{\text{3}}{\text{8}}$

Therefore, the required percentage of coloured parts,

 is $\text{= }\frac{\text{3}}{\text{8}}\text{  }\!\!\times\!\!\text{  }\frac{\text{100}}{\text{100}}$

$\text{= }\frac{\text{300}}{\text{8}}\text{ }\%$

$\text{= 37}\text{.5 }\%$

4. Find: 

(a) $\text{15 }\%$ of $\text{250}$

Ans: Needed to find the required percentage of the given number $\text{250}$ i.e.,

$\text{15 }\%\text{  }$ of $\text{250}$ $\text{= }\frac{\text{15}}{\text{100}}\text{  }\!\!\times\!\!\text{  250}$

$\text{= 15  }\!\!\times\!\!\text{  2}\text{.5}$

$\text{= 37}\text{.5}$

$\Rightarrow \text{ 15 }\%\text{  }$ of $\text{250}$$\text{= 37}\text{.5}$

(b). $\text{1 }\%$ of $\text{1}$ hour

Ans: Needed to find the required percentage i.e.,

$\text{1 }\%$ of $\text{1}$ hour $\text{= 1 }\%$ of $\text{60}$ minutes

$\text{= 1 }\%$ of $\text{60  }\!\!\times\!\!\text{  60}$ seconds

$\text{= }\frac{\text{1}}{\text{100}}\text{  }\!\!\times\!\!\text{  60  }\!\!\times\!\!\text{  60}$ seconds

$\text{= 36}$ seconds

$\Rightarrow \text{1 }\%$ of $\text{1}$ hour $\text{= 36}$ seconds

(c). $\text{20 }\%$ of Rs$\text{2500}$

Ans: Needed to find the required percentage of the given currency Rs$\text{2500}$ i.e.,

$\text{20 }\%$ of Rs$\text{2500}$ $\text{= }\frac{\text{20}}{\text{100}}\text{  }\!\!\times\!\!\text{  2500}$

$\text{= 20  }\!\!\times\!\!\text{  25}$

$\text{=}$ Rs $\text{500}$

$\Rightarrow \text{20 }\%$ of Rs$\text{2500}$$\text{=}$Rs$\text{500}$

(d). $\text{75 }\%$ of $\text{1}$ kg

Ans: Needed to find the required percentage of the given quantity $\text{1}$ kg i.e.,

$\text{75 }\%$ of $\text{1}$ kg $\text{= }\frac{75}{\text{100}}\text{  }\!\!\times\!\!\text{  1}$ kg

$\text{= 0}\text{.75}$kg

$\Rightarrow \text{75 }\%$ of $\text{1}$ kg $\text{= 0}\text{.75}$kg

5. Find the whole quantity if: 

(a). $\text{5 }\%$ of it is $\text{600}$

Ans: Let the required whole quantity be $\text{x}$

Therefore, $\text{5 }\%$ of $\text{x}$ $\text{= 600}$

$\Rightarrow \text{ }\frac{\text{5}}{\text{100}}\text{  }\!\!\times\!\!\text{  x = 600}$

$\Rightarrow \text{ x = }\frac{\text{600  }\!\!\times\!\!\text{  100}}{\text{5}}$

$\Rightarrow \text{ x = 12000}$

(b). $\text{12 }\%$ of it is Rs$\text{1080}$

Ans: Let the required whole quantity be $\text{x}$

Therefore, $\text{12 }\%$ of $\text{x}$ $\text{= Rs 1080}$

$\Rightarrow \text{ }\frac{\text{12}}{\text{100}}\text{  }\!\!\times\!\!\text{  x = 1080}$

$\Rightarrow \text{ x = }\frac{\text{1080  }\!\!\times\!\!\text{  100}}{\text{12}}$

$\Rightarrow \text{ x = Rs 9000}$

(c). $\text{40 }\%$ of it is $\text{500}$ km

Ans: Let the required whole quantity be $\text{x}$

Therefore, $\text{40 }\%$ of $\text{x}$ $\text{= 500}$km

$\Rightarrow \text{ }\frac{\text{40}}{\text{100}}\text{  }\!\!\times\!\!\text{  x = 500}$

$\Rightarrow \text{ x = }\frac{\text{500  }\!\!\times\!\!\text{  100}}{\text{40}}$

$\Rightarrow \text{ x = 1250}$km

(d). $\text{70 }\%$ of it is $\text{14}$ minutes

Ans: Let the required whole quantity be $\text{x}$

Therefore, $\text{70 }\%$ of $\text{x}$ $\text{= 14}$minutes

$\Rightarrow \text{ }\frac{\text{70}}{\text{100}}\text{  }\!\!\times\!\!\text{  x = 14}$

$\Rightarrow \text{ x = }\frac{\text{14  }\!\!\times\!\!\text{  100}}{\text{70}}$

$\Rightarrow \text{ x = 20}$ minutes

(e). $\text{8 }\%$ of it is $\text{40}$ liters

Ans: Let the required whole quantity be $\text{x}$

Therefore, $\text{8 }\%$ of $\text{x}$ $\text{= 40}$liters

$\Rightarrow \text{ }\frac{\text{8}}{\text{100}}\text{  }\!\!\times\!\!\text{  x = 40}$

$\Rightarrow \text{ x = }\frac{\text{40  }\!\!\times\!\!\text{  100}}{\text{8}}$

$\Rightarrow \text{ x = 500}$ liters

6. Convert given percents to decimal fractions and also fractions to simplest form:

(a). $\text{25 }\%$

Ans: We have given a percent $\text{25 }\%$ 

Fraction form$\text{= }\frac{\text{25}}{\text{100}}$

Simplest fractional form $\text{= }\frac{\text{1}}{\text{4}}$

Decimal form $\text{= 0}\text{.25}$

(b). $\text{150 }\%$

Ans: We have given a percent $\text{150 }\%$ 

Fraction form $\text{= }\frac{\text{150}}{\text{100}}$

Simplest fractional form $\text{= }\frac{\text{3}}{\text{2}}$

Decimal form $\text{= 1}\text{.5}$

(c). $\text{20 }\%$

Ans: We have given a percent $\text{20 }\%$ 

Fraction form $\text{= }\frac{\text{20}}{\text{100}}$

Simplest fractional form $\text{= }\frac{\text{1}}{\text{5}}$

Decimal form $\text{= 0}\text{.2}$

(d). $\text{5 }\%$

Ans: We have given a percent $\text{5 }\%$ 

Fraction form $\text{= }\frac{\text{5}}{\text{100}}$

Simplest fractional form $\text{= }\frac{\text{1}}{\text{20}}$

Decimal form $\text{= 0}\text{.05}$

7. In a city, $\text{30 }\%$ are females, $\text{40 }\%$ are males and remaining are children. What percent are children?

Ans:  Let the percentage of children be $\text{x  }\%$ 

It is given that the percentage of females and males are $\text{30 }\%$ and $\text{40 }\%$ respectively.

And, the total percentage $\text{= 100 }\%\text{  =}$ Percentage of males and Percentage of females and Percentage of children

$\Rightarrow \text{ 100 }\%\text{  = 30 }\%\text{  + 40 }\%\text{  + x }\%$

$\Rightarrow \text{ 100 }\%\text{  = 70 }\%\text{  + x }\%$

$\Rightarrow \text{ x }\%\text{   = 100 }\%\text{  - 70 }\%\text{  }$

$\Rightarrow \text{ x }\%\text{  = 30 }\%$

Thus $\text{30 }\%\text{  }$is the population of children in the city.

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

Ans: The total number of voters $\text{= 15,000}$

The percentage of people who voted $\text{= 60 }\%$

So, the percentage of people who didn’t vote $\text{= 100 }\%\text{  - 60 }\%$ 

$\text{= 40 }\%$

And, the number of actual candidates, who didn’t vote $=40 \%$ of $\text{15000}$ 

$\text{= 6000}$

Thus, $\text{6,000}$ people out of $\text{15,000}$ did not vote.

9. Meeta saves Rs $\text{400}$ from her salary. If this is $\text{10 }\%$ of her salary. What is her salary?

Ans:  Let $\text{x}$ be the salary of Meeta.

Since $\text{10 }\%$ of her salary $\text{= Rs 400}$

$\Rightarrow \text{ 10 }\%\text{  of x = 400}$

$\Rightarrow \text{ 10 }\%\text{   }\!\!\times\!\!\text{  x = 400}$

$\Rightarrow \text{ }\frac{\text{10}}{\text{100}}\text{x = 400}$

$\Rightarrow \text{ x = Rs 4,000}$

Therefore, the salary of Meeta is $\text{Rs 4,000}$.

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

Ans: The local cricket team played $\text{20}$ matches.

They won $\text{25 }\%$ of matches out of $\text{20}$ 

Therefore, the number of matches the cricket team won $\text{= 25  }\%\text{  of  20}$

$\text{= }\frac{\text{25}}{\text{100}}\text{  }\!\!\times\!\!\text{  20}$

$\text{= 5}$ matches

So, the local cricket team won $\text{5}$ matches out of $\text{20}$.

Conclusion

In Class 7 Maths Chapter 7 Exercise 7.1 provides a solid understanding of comparing quantities using ratios and percentages. Maths Class 7 Chapter 7 Exercise 7.1 helps students grasp the basics of these concepts and apply them in various contexts. By working through the problems, students build confidence in their ability to compare different quantities accurately, setting a strong foundation for more advanced topics.

Class 7 Maths Chapter 7: Exercises Breakdown

CBSE Class 7 Maths Chapter 7 Other Study Materials

Chapter-Specific NCERT Solutions for Class 7 Maths

Given below are the chapter-wise NCERT Solutions for Class 7 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.