Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 8 Comparing Quantities Ex 8.1 Textbook Exercise Questions and Answers.
PSEB Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.1
1. Find the ratio of the following.
Question (a).
Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour.
Solution:
Speed of a cycle = 15 km/h
Speed of a scooter = 30 km / h
∴ Ratio of the speed of a cycle to the speed of a scooter
= \(\frac{15 \mathrm{~km} / \mathrm{h}}{30 \mathrm{~km} / \mathrm{h}}\)
= \(\frac {1}{2}\)
= 1 : 2
Question (b).
5 m to 10 km
Solution:
[Note : Unit of both quantities should be same.]
1 km = 1000 m
∴ 10 km = 10 × 1000 m
= 10,000 m
∴ Ratio of 5 m to 10 km = \(\frac{5 \mathrm{~m}}{10 \mathrm{~km}}\)
= \(\frac{5 \mathrm{~m}}{10000 \mathrm{~m}}\)
= \(\frac{1}{2000}\)
= 1 : 2000
Question (c).
50 paise to ₹ 5
Solution:
[Note : Unit of both quantities should be same.]
₹ 1 = 100 paise
∴ ₹ 5 = 500 paise
∴ Ratio of 50 paise to ₹ 5 = \(\frac{50 \text { paise }}{₹ 5}\)
= \(\frac{50 \text { paise }}{500 \text { paise }}\)
= \(\frac{1}{10}\)
= 1 : 10
2. Convert the following ratios to percentages.
Question (a).
3 : 4
Solution:
Given ratio = 3 : 4
∴ Percentage = (\(\frac{3}{4}\) × 100) %
= (3 × 25) %
= 75 %
Question (b).
2 : 3
Solution:
Given ratio = 2 : 3
∴ Percentage = (\(\frac{2}{3}\) × 100) %
= (\(\frac{200}{3}\)) %
= 66 \(\frac{2}{3}\)%
3. 72% of 25 students are interested in Mathematics. How many are not interested in Mathematics?
Solution:
Total number of students = 25
Students interested in Mathematics = 72%
∴ Students who are not interested in Mathematics = (100 – 72) %
= 28 %
Number of students who are not interested in Mathematics = 28% of 25
= \(\frac{28}{100}\) × 25
= \(\frac{28}{4}\)
= 7
Thus, 7 students are not interested 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:
Number of matches won by the football team = 10
Let x matches be played by the team.
∴ 40% of x = 10
∴ \(\frac{40}{100}\) × x = 10
∴ x = \(\frac{10 \times 100}{40}\)
= 25
Thus, the football team played 25 matches in all.
5. If Chameli had ₹ 600 left after spending 75% of her money, how much did she have in the beginning?
Solution:
Let Chameli had in the beginning ₹ x
Percentage of money spent by Chameli = 75 %
Percentage of money left with Chameli = (100 – 75)%
= 25%
But money left = ₹ 600 (Given)
∴ 25% of x = 600
∴ \(\frac{25}{100}\) × x = 600
∴ x = \(\frac{600 \times 100}{25}\)
∴ x = 2400
Thus, Chameli had ₹ 2400 in the beginning.
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 is 50 lakh, find the exact number who like each type of game.
Solution:
Percentage of people who like cricket = 60 %
Percentage of people who like football = 30 %
∴ Percentage of people who like other games = [ 100 – (60 + 30)]%
= (100 – 90)%
= 10 %
Total number of people = 50,00,000 (Given)
Now,
People who like cricket
= 60% of 50,00,000
= \(\frac {1}{2}\) × 50,00,000
= 60 × 50000
= 3000000
= 30 lakh
People who like football
= 30% of 5000000
= \(\frac {30}{100}\) × 5000000
= 30 × 50000
= 1500000
= 15 lakh
People who like other games
= 10% of 5000000
= \(\frac {10}{100}\) × 5000000
= 500000
= 5 lakh
Thus, number of people who like
cricket = 30 lakh,
football = 15 lakh
and other games = 5 lakh