GSEB Solutions Class 8 Maths Chapter 8 Comparing Quantities Ex 8.1

Gujarat Board 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 ₹5
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 = $$\frac{5m}{10×1000m}$$ (Changing 10 km into m)
= $$\frac{5}{10×1000}$$ = $$\frac{1}{2000}$$ (or 1 : 2000)

(c) $$\frac{50 \text { paise }}{₹ 5}=\frac{50 \text { paise }}{500 \text { paise }}$$ (Changing ₹ 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) ∵ 3 : 4 = $$\frac{3}{4}$$
∴ $$\frac{3}{4}$$ = $$\frac{3}{4}$$ × 100% = (3 × 25)% = 75%

(b) ∵ 2 : 3 = $$\frac{2}{3}$$
∴ $$\frac{2}{3}$$ = $$\frac{2}{3}$$ × 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:
∵ 72% of 25 are good in Mathematics.
∴ (100 – 72)% of 25 students are not good in Mathematics.
or 28% of 25 students are not good in Mathematics
or $$\frac{28}{100}$$ × 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
∵ The team won 40% of total number of matches.
∴ 40% of [Total number of matches] = 10
or $$\frac{40}{100}$$ × [Total number of matches] = 10
or Total number of matches = $$\frac{10×100}{40}$$ = 25
Thus, the total number of matches played = 25

Question 5.
If Chameli had ₹ 600 left after spending 75% of her money how much did she have in the beginning?
Solution:
∵ Chameli made spending of ₹ 75%.
∴ She is left with ₹ (100 – 75)% or ₹ 25%.
But she is having ₹ 600 now.
∴ 25% of total money = ₹ 600
or total money = ₹ $$\frac{600×100}{25}$$
= ₹ 600 × 4 = ₹ 2400
Thus, she had ₹ 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:
∵ People who like cricket = 60%
People who like football = 30%
∴ People who like other games
[100 – (60 + 30)]%
= [100 – 90]% = 10%
Now, total number of people = 50.00,000
∴ 60% of 50,00,000 = $$\frac{60}{100}$$ × 5000000
= 6 × 5000000 = 30,00,000
30% of 5000000 = $$\frac{30}{100}$$ × 5000000
= 3 × 5000000 = 15,00,000
10% of 5000000 = $$\frac{10}{100}$$ × 5000000
= 1 × 5000000 = 5,00,000
Cricket = 30,00,000
Football = 15,00,000
Other games = 5,00,000