NCERT Solutions Class 8th Maths Chapter – 7 Comparing Quantities Exercise – 7.1

1. Find the ratio of the following:

(a) Speed of a cycle 15 km per hour to the speed of a scooter 30 km per hour.

(b) 5 m to 10 km

(c) 50 paise to ₹ 5

Solution:

(a) Ratio of the speed of cycle to the speed of scooter = 15/30 = ½ = 1:2

(b) Since, 1 km = 1000m
5m/10km = 5m/(10 x 1000)m = 5/10000 = 1/2000 = 1:2000
The required ratio is 1: 2000

(c) Since, ₹1 = 100 paise
50 paise/₹5 = 50/(5 x 100) = 50/500 = 1/10 = 1:10
The required ratio is 1: 10

2. Convert the following ratio to percentages

(a) 3:4
(b) 2:3

Solution:

(a) 3:4 = ¾ = ¾ x 100% = 0.75 x 100% = 75%

(b) 2:3 = 2/3 = 2/3 x 100% = 0.666 x 100% = 66.66% = 66⅔%

3. 72% of 25 students are good in mathematics. How many are not good in mathematics?

Solution: 

It’s given that 72% of 25 students are good in mathematics
So, the percentage of students who are not good in mathematics = (100 – 72)%
= 28%

Here, number of students who are good in mathematics = 72/100 x 25 = 18
Thus, the number of students who are not good in mathematics = 25 – 18 = 7
[Also, 28% of 25 = 28/100 x 25 = 7]
Therefore, 7 students are not good in mathematics.

4. A football team won 10 matches out of the total number of matches they played. If their win percentage was 40, then how many matches did they play in all?

Solution: 

Let the total number of matches played by the team be x.
Given that the team won 10 matches and the winning percentage of the team was 40%.
⇒ 40/100 × x = 10
40x = 10 × 100
40x = 1000
x = 1000/40
= 100/4
= 25
Therefore, the team played 25 matches.

5. If Chameli had ₹600 left after spending 75% of her money, how much did she have in the beginning?

Solution: 

Let the amount of money which Chameli had in the beginning be x
Given that, after spending 75% of ₹x, she was left with ₹600
So, (100 – 75)% of x = ₹600
Or, 25% of x = ₹600
25/100 × x = ₹600
x = ₹600 × 4
= ₹2400
Therefore, Chameli had ₹2400 is the beginning.

6. If 60% people in city like cricket, 30% like football and the remaining like other games, then what per cent of the people like other games? If the total number of people are 50 lakh, find the exact number who like each type of game.

Solution: 

Percentage of people who like other games = (100 – 60 – 30)%
= (100 – 90)%
= 10%
Total number of people = 50 lakhs
So,
Number of people who like cricket = 60/100 x 50 = 30 lakhs
Number of people who like football = 30/100 x 50 = 15 lakhs
Number of people who like other games = 10/100 x 50 = 5 lakhs