These NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.1 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Exercise 8.1
Question 1.
Find the ratio of the following:
(a) Speed of a cycle 15km per hour to the speed of scooter 30 km per hour.
(b) 5 m to 10 km
(c) 50 paise to ₹ 5
Solution:
(a) Speed of the cycle = 15 km per hour.
Speed of the scooter = 30 km per hour.
∴ Ratio = Speed of the cycle : Speed of the scooter
= 15 : 30
= 1 : 2 (Divided by 15)
(b) 10 km = 10 × 1000 m = 10000 m
Ratio = 5 m : 10 km
= 5 : 10000
= 1 : 2000
(c) ₹ 5 = 5 × 100 paise = 500 paise
Ratio = 50 paise : ₹ 5
= 50 : 500
= 1 : 10
Question 2.
Convert the following ratios to percentages.
(a) 3 : 4
(b) 2 : 3
Solution:
(a) 3 : 4 = \(\frac{3}{4}\)
= \(\frac{3}{4}\) × 100%
= 75%
(b) 2 : 3 = \(\frac{2}{3}\)
= \(\frac{2}{3}\) × 100
= \(\frac{200}{3}\)
= 66\(\frac{2}{3}\) %
Question 3.
72% of 25 students are good at mathematics. How many are not good in mathematics.
Solution:
Total number of students = 25
Number of students good in mathematics = 72% of 25
= \(\frac{72}{100}\) × 25
= 18
Number of students who are not good in mathematics = 25 – 18 = 7
Percentage of students not good in mathematics = \(\frac{7}{25}\) × 100
= 7 × 4
= 28%
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
Let the total number of matches be ‘x’
The team won 40% the total number matches.
∴ \(\frac{40}{100}\) × x = 10
x = \(\frac{10 \times 100}{40}\) = 25
∴ 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:
Amount left with Chameli = (100 – 75)% = 25%
Let the total amount with Chameli be ₹ ‘x’
∴ 25% of total money = ₹ 600
\(\frac{25}{100}\) × x = 600
x = \(\frac{600 \times 100}{25}\) = ₹ 2400
Amount in the beginning = ₹ 2400
Question 6.
If 60% of people in a city like a cricket 30% like football and the remaining like other games, then what percent 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:
People who like cricket = 60%
People who like football = 30%
People who like other games = 100 – (60 + 30)
= 100 – 90
= 10%
Total number of people = 50,00,000
No. of people who like cricket = \(\frac{60}{100}\) × 50,00,000 = 30,00,000
No. of people who like football = \(\frac{30}{100}\) × 50,00,000 = 15,00,000
No. of people who like other games = \(\frac{10}{100}\) × 50,00,000 = 5,00,000