Examples (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

Example 1

Write $\frac{1}{3}$ as per cent.
Solution

We have, $\frac{1}{3}=\frac{1}{3} \times \frac{100}{100}=\frac{1}{3} \times 100 \%$
$
=\frac{100}{3} \%=33 \frac{1}{3} \%
$

Example 2

Out of 25 children in a class, 15 are girls. What is the percentage of girls?
Solution Out of 25 children, there are 15 girls.
Therefore, percentage of girls $=\frac{15}{25} \times 100=60$. There are $60 \%$ girls in the class.
Example 3

Convert $\frac{5}{4}$ to per cent.
Solution

We have, $\frac{5}{4}=\frac{5}{4} \times 100 \%=125 \%$

From these examples, we find that the percentages related to proper fractions are less than 100 whereas percentages related to improper fractions are more than 100 .

Example 4

Convert the given decimals to per cents:
(a) 0.75
(b) 0.09
(c) 0.2

Solution
(a) $0.75=0.75 \times 100 \%$
(b) $0.09=\frac{9}{100}=9 \%$
$
=\frac{75}{100} \times 100 \%=75 \%
$
(c) $0.2=\frac{2}{10} \times 100 \%=20 \%$

Example 5

What per cent of the adjoining figure is shaded?
Solution

We first find the fraction of the figure that is shaded. From this fraction, the percentage of the shaded part can be found.

You will find that half of the figure is shaded. And, $\frac{1}{2}=\frac{1}{2} \times 100 \%=50 \%$ Thus, $50 \%$ of the figure is shaded.

Example 6

A survey of 40 children showed that $25 \%$ liked playing football. How many children liked playing football?

Solution

Here, the total number of children are 40 . Out of these, $25 \%$ like playing football. Meena and Arun used the following methods to find the number. You can choose either method.

Arun does it like this
Out of 100,25 like playing football
So out of 40 , number of children who like playing football $=\frac{25}{100} \times 40=10$ 

Meena does it like this $25 \%$ of $40=\frac{25}{100} \times 40$ $=10$

Hence, 10 children out of 40 like playing football.

Example 7

Rahul bought a sweater and saved $₹ 200$ when a discount of $25 \%$ was given. What was the price of the sweater before the discount?

Solution

Rahul has saved ₹ 200 when price of sweater is reduced by $25 \%$. This means that $25 \%$ reduction in price is the amount saved by Rahul. Let us see how Mohan and Abdul have found the original cost of the sweater.
Mohan's solution
$25 \%$ of the original price $=₹ 200$
Let the price (in ₹) be $P$
So, $25 \%$ of $P=200$ or $\frac{25}{100} \times P=200$
or, $\frac{P}{4}=200$ or $P=200 \times 4$
Therefore, $P=800$
Abdul's solution
$₹ 25$ is saved for every ₹ 100
Amount for which ₹ 200 is saved
$
=\frac{100}{25} \times 200=₹ 800
$

Thus both obtained the original price of sweater as ₹ 800 .

Example 8

Reena's mother said, to make idlis, you must take two parts rice and one part urad dal. What percentage of such a mixture would be rice and what percentage would be urad dal?

Solution

In terms of ratio we would write this as Rice : Urad dal $=2: 1$.
Now, $2+1=3$ is the total of all parts. This means $\frac{2}{3}$ part is rice and $\frac{1}{3}$ part is urad dal.
Then, percentage of rice would be $\frac{2}{3} \times 100 \%=\frac{200}{3}=66 \frac{2}{3} \%$.
Percentage of urad dal would be $\frac{1}{3} \times 100 \%=\frac{100}{3}=33 \frac{1}{3} \%$.

Example 9

If ₹ 250 is to be divided amongst Ravi, Raju and Roy, so that Ravi gets two parts, Raju three parts and Roy five parts. How much money will each get? What will it be in percentages?

Solution

The parts which the three boys are getting can be written in terms of ratios as $2: 3: 5$. Total of the parts is $2+3+5=10$.

Example 10

A school team won 6 games this year against 4 games won last year. What is the per cent increase?

Solution

The increase in the number of wins (or amount of change) $=6-4=2$.
$
\begin{aligned}
\text { Percentage increase } & =\frac{\text { amount of change }}{\text { original amount or base }} \times 100 \\
& =\frac{\text { increase in the number of wins }}{\text { original number of wins }} \times 100=\frac{2}{4} \times 100=50
\end{aligned}
$

Example 11

The number of illiterate persons in a country decreased from 150 lakhs to 100 lakhs in 10 years. What is the percentage of decrease?

Solution

Original amount $=$ the number of illiterate persons initially $=150$ lakhs.

Amount of change $=$ decrease in the number of illiterate persons $=150-100=50$ lakhs Therefore, the percentage of decrease
$
=\frac{\text { amount of change }}{\text { original amount }} \times 100=\frac{50}{150} \times 100=33 \frac{1}{3}
$