Exercise 7.1 (Revised) - Chapter 7 Comparing Quantities class 7 ncert solutions Maths - SaraNextGen [2024-2025]

Updated On August 15, 2024

By SaraNextGen

Chapter 7 - Comparing Quantities | NCERT Solutions Class 7 Maths

Ex 7.1 Question 1.

Convert the given fractional numbers to percent:
(a) $\frac{1}{8}$
(b) $\frac{5}{4}$
(c) $\frac{3}{40}$
(d) $\frac{2}{7}$

Answer:

(a) $\frac{1}{8}=\frac{1}{8} \times 100 \%=\frac{25}{2} \%=12.5 \%$
(b) $\frac{5}{4}=\frac{5}{4} \times 100 \%=5 \times 25 \%=125 \%$
(c) $\frac{3}{40}=\frac{3}{40} \times 100 \%=\frac{3}{2} \times 5 \%=\frac{15}{2} \%=7.5 \%$
(d) $\frac{2}{7}=\frac{2}{7} \times 100 \%=\frac{200}{7} \%=28 \frac{4}{7} \%$

Ex 7.1 Question 2.

Convert the given decimal fractions to percents:
(a) 0.65
(b) 2.1
(c) 0.02
(d) 12.35

Answer:

(a) $0.65=\frac{65}{100} \times 100 \%=65 \%$

(b) $2.1=\frac{21}{10} \times 100 \%=210 \%$
(c) $0.02=\frac{2}{100} \times 100 \%=2 \%$
(d) $12.35=\frac{1235}{100} \times 100 \%=1235 \%$

Ex 7.1 Question 3.

Estimate what part of the figures is coloured and hence find the percent which is coloured:

Answer:

(i) Coloured part $=\frac{1}{4}$
$\therefore$ Percent of coloured part $=\frac{1}{4} \times 100 \%=25 \%$

(ii) Coloured part $=\frac{3}{5}$
$\therefore$ Percent of coloured part $=\frac{3}{5} \times 100 \%=60 \%$

(iii) Coloured part $=\frac{3}{8}$
$\therefore$ Percent of coloured part $=\frac{3}{8} \times 100 \%=\frac{3}{2} \times 25 \%$
$
=37.5 \%
$

Ex 7.1 Question 4.

Find: 

(a) $15 \%$ of 250
(b) $1 \%$ of 1 hour
(c) $20 \%$ of Rs. 2500
(d) $75 \%$ of $1 \mathrm{~kg}$

Answer:

(a) $15 \%$ of $250=\frac{15}{100} \times 250=15 \times 2.5=37.5$
(b) $1 \%$ of 1 hours $=1 \%$ of 60 minutes $=1 \%$ of $(60 \times 60)$ seconds
$
=\frac{1}{100} \times 60 \times 60=6 \times 6=36 \text { seconds }
$
(c) $20 \%$ of Rs. $2500=\frac{20}{100} \times 2500=20 \times 25=$ Rs. 500
(d) $75 \%$ of $1 \mathrm{~kg}=75 \%$ of $1000 \mathrm{~g}=\frac{75}{100} \times 1000=750 \mathrm{~g}=0.750 \mathrm{~kg}$

Ex 7.1 Question 5.

Find the whole quantity if:
(a) $5 \%$ of it is 600
(b) $12 \%$ of it is Rs. 1080
(c) $40 \%$ of it is $500 \mathrm{~km}$
(d) $70 \%$ of it is 14 minutes
(e) $8 \%$ of it is 40 liters

Answer:

Let the whole quantity be $x$ in given questions:

(a) $5 \%$ of $x=600$
$
\begin{aligned}
& \Rightarrow \frac{5}{100} \times x=600 \\
& \Rightarrow x=\frac{600 \times 100}{5}=12,000
\end{aligned}
$
(b) $12 \%$ of $x=$ Rs. 1080
$
\Rightarrow \frac{12}{100} \times x=1080
$

$
\Rightarrow x=\frac{1080 \times 100}{12}=\text { Rs. } 9,000
$
$
\begin{aligned}
& \text { (c) } 40 \% \text { of } x=500 \mathrm{~km} \\
& \Rightarrow \frac{40}{100} \times x=500 \\
& \Rightarrow x=\frac{500 \times 100}{40}=1,250 \mathrm{~km}
\end{aligned}
$
(d) $70 \%$ of $x=14$ minutes
$
\begin{aligned}
& \Rightarrow \frac{70}{100} \times x=14 \\
& \Rightarrow x=\frac{14 \times 100}{70}=20 \text { minutes }
\end{aligned}
$
(e) $8 \%$ of $x=40$ liters
$
\begin{aligned}
& \Rightarrow \frac{8}{100} \times x=40 \\
& \Rightarrow x=\frac{40 \times 100}{8}=500 \text { liters }
\end{aligned}
$

Ex 7.1 Question 6.

Convert given percents to decimal fractions and also to fractions in simplest forms:
(a) $25 \%$
(b) $150 \%$
(c) $20 \%$
(d) $5 \%$

Answer:

Ex 7.1 Question 7.

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

Given: Percentage of females $=30 \%$
Percentage of males $=40 \%$
Total percentage of females and males $=30+40=70 \%$
Percentage of children $=$ Total percentage - Percentage of males and females
$
\begin{aligned}
& =100 \%-70 \% \\
& =30 \%
\end{aligned}
$

Hence, $30 \%$ are children.
Ex 7.1 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?

Answer:

Total voters $=15,000$
Percentage of voted candidates $=60 \%$
Percentage of not voted candidates $=100 \%-60 \%=40 \%$
Actual candidates, who did not vote $=40 \%$ of $15000=\frac{40}{100} \times 15000=6,000$
Hence, 6,000 candidates did not vote.

Ex 7.1 Question 9.

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

Answer:

Let Meera's salary be Rs. $x$.

Now, $10 \%$ of salary = Rs. 400
$
\begin{aligned}
& \Rightarrow 10 \% \text { of } x=\text { Rs. } 400 \\
& \Rightarrow \frac{10}{100} \times x=400 \\
& \Rightarrow x=\frac{400 \times 100}{10}
\end{aligned}
$

$
\Rightarrow x=4,000
$

Hence, Meera's salary is Rs. 4,000 .
Ex 7.1 Question 10.

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

Answer:

Number of matches played by cricket team $=20$
Percentage of won matches $=25 \%$
Total matches won by them $=25 \%$ of $20=\frac{25}{100} \times 20=5$
Hence, they won 5 matches.