Gujarat BoardĀ GSEB Textbook Solutions Class 8 Maths Chapter 8 Comparing Quantities Ex 8.1 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 8 Maths Chapter 8 Comparing Quantities Ex 8.1

Question 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.

(b) 5 m to 10 km

(c) 50 paise to ā¹5

Solution:

In a ratio, the quantities are in the same unit. If they are not in the same units, then first we convert them in the same unit.

(a) Speed of cycle = 15 km per hour

Speed of scooter = 30 km per hour Speed of cycle

= \(\frac{15km/hr}{30km/hr}\) = \(\frac{15}{30}\) = \(\frac{1}{2}\) (or 1 : 2)

(b) Ratio = \(\frac{5m}{10Ć1000m}\) (Changing 10 km into m)

= \(\frac{5}{10Ć1000}\) = \(\frac{1}{2000}\) (or 1 : 2000)

(c) \(\frac{50 \text { paise }}{ā¹ 5}=\frac{50 \text { paise }}{500 \text { paise }}\) (Changing ā¹ 5 to paise)

= \(\frac{50}{500}\) = \(\frac{1}{10}\) (0r 1 : 10)

Question 2.

Convert the following ratios to percentages?

(a) 3 : 4

(b) 2 : 3

Solution:

(a) āµ 3 : 4 = \(\frac{3}{4}\)

ā“ \(\frac{3}{4}\) = \(\frac{3}{4}\) Ć 100% = (3 Ć 25)% = 75%

(b) āµ 2 : 3 = \(\frac{2}{3}\)

ā“ \(\frac{2}{3}\) = \(\frac{2}{3}\) Ć 100% = \(\frac{200}{3}\)% = 66\(\frac{2}{3}\)%

Question 3.

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

Solution:

āµ 72% of 25 are good in Mathematics.

ā“ (100 – 72)% of 25 students are not good in Mathematics.

or 28% of 25 students are not good in Mathematics

or \(\frac{28}{100}\) Ć 25 = 7 students are not good in Mathematics.

Question 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:

Number of matches won by the team = 10

āµ The team won 40% of total number of matches.

ā“ 40% of [Total number of matches] = 10

or \(\frac{40}{100}\) Ć [Total number of matches] = 10

or Total number of matches = \(\frac{10Ć100}{40}\) = 25

Thus, the total number of matches played = 25

Question 5.

If Chameli had ā¹ 600 left after spending 75% of her money how much did she have in the beginning?

Solution:

āµ Chameli made spending of ā¹ 75%.

ā“ She is left with ā¹ (100 – 75)% or ā¹ 25%.

But she is having ā¹ 600 now.

ā“ 25% of total money = ā¹ 600

or total money = ā¹ \(\frac{600Ć100}{25}\)

= ā¹ 600 Ć 4 = ā¹ 2400

Thus, she had ā¹ 2400 in the beginning.

Question 6.

If 60% people in a 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:

āµ People who like cricket = 60%

People who like football = 30%

ā“ People who like other games

[100 – (60 + 30)]%

= [100 – 90]% = 10%

Now, total number of people = 50.00,000

ā“ 60% of 50,00,000 = \(\frac{60}{100}\) Ć 5000000

= 6 Ć 5000000 = 30,00,000

30% of 5000000 = \(\frac{30}{100}\) Ć 5000000

= 3 Ć 5000000 = 15,00,000

10% of 5000000 = \(\frac{10}{100}\) Ć 5000000

= 1 Ć 5000000 = 5,00,000

Cricket = 30,00,000

Football = 15,00,000

Other games = 5,00,000