Mathematics – Class 8 – Chapter 8 – Comparing Quantities – Exercise 8.1 – NCERT Exercise Solution

1. Find the ratio of the following:

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

Solution:

According to the question:

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

(b) 5 m to 10 km

Solution:

1 km = 1000m

Now,

5m/10km = 5m/(10 x 1000)m

                  = 5/10000

                 = 1/2000 = 1:2000

Hence the required ratio is 1: 2000

(c) 50 paise to ₹ 5

Solution:

₹1 = 100 paise

50 paise/₹5 = 50/(5 x 100)

                 = 50/500

               = 1/10 = 1:10

Hence, the required ratio is 1: 10

2. Convert the following ratio to percentages

a) 3:4

Solution:

3:4 = ¾

Now,

= ¾ x 100%

= 0.75 x 100%

= 75%

b) 2:3

Solution:

 2:3 = 2/3

Now,

= 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:

Given, 72% of 25 students are good in mathematics

Let the total student = 100 %

So, the percentage of students who are not good in mathematics = (100 – 72)%

                                                                                                          = 28%

Now,

Here, number of students who are good in mathematics = 72/100 x 25

= 18

Hence, the number of students who are not good in mathematics = 25 – 18

                                                                                                           = 7

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 us assume total number of matches played by the team be x.

Given, the team won 10 matches and the winning percentage of the team was 40%.

Now,

40/100 × x = 10

40x = 10 × 100

40x = 1000

x = 1000/40

= 100/4

= 25

Hence, 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 us assume the amount of money which Chameli had in the beginning be x

Given, after spending 75% of ₹x, ₹600 was left with her

So, (100 – 75)% of x = ₹600

 25% of x = ₹600

25/100 × x = ₹600

1/4 × x = ₹600

x = ₹600 × 4

= ₹2400

Hence, 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:

Let us assume total % of people = 100

Percentage of people who like other games = (100 – 60 – 30)%

                                                                      = (100 – 90)%

                                                                       = 10%

Given, total number of people = 50 lakhs

Hence,

Total number of people who like cricket = 60/100 x 50 = 30 lakhs

Total number of people who like football = 30/100 x 50 = 15 lakhs

Total number of people who like other games = 10/100 x 50 = 5 lakhs

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