Class 8 Maths Chapter 8 Comparing Quantities Exercise 8.1 Solution of NCERT
Introduction :
In this exercise 8.1, we will learn about ratio. Ratio means comparing two Quantities.
Class 8 Maths Chapter 8 Comparing Quantities :
- NCERT Class 8 Maths Chapter 8 Comparing Quantities Exercise 8.1
- NCERT Class 8 Maths Chapter 8 Comparing Quantities Exercise 8.2
- NCERT Class 8 Maths Chapter 8 Comparing Quantities Exercise 8.3
NCERT Class 8 Maths Exercise 8.1 (Page-119)
Q1. 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 paisa to ₹ 5
Solution:
a) Speed of cycle = 15km/hr
Speed of scooter = 30km/hr
So, the ratio of speed of cycle to the speed of scooter = \(\displaystyle \frac{{15}}{{30}}\)
= \(\displaystyle \frac{{1}}{{2}}\)
hence, the answer is 1:2.
b) To find the ratio we should have same quantities. So, we will convert 10km into m.
1km = 1000m
10km = 10000m
So, the ratio of 5m to 10km = \(\displaystyle \frac{{5}}{{10000}}\)
=\(\displaystyle \frac{{1}}{{2000}}\)
hence, the answer is 1:2000.
c) To find the ratio we should have same quantities. So, we will convert Rs 5 into paisa
1 Rs = 100 paisa
5 Rs = 500 paisa
So, the ratio of 50 paisa to ₹ 5= \(\displaystyle \frac{{5}}{{500}}\)
= \(\displaystyle \frac{{1}}{{100}}\)
hence, the answer is 1:100.
Class 8 Maths Chapter 8 Comparing Quantities Exercise 8.1 Solution of NCERT
Q2. Convert the following ratios to percentages:
(a) 3 : 4
(b) 2 : 3
Solution:
a) 3: 4 = 
= 3 \(\displaystyle \times \) 25
= 75 %
b) 2:3 = 
= \(\displaystyle \frac{{200}}{3}\)
= \(\displaystyle 66\frac{2}{3}\)%
Q3. 72% of 25 students are good in mathematics. How many are not good in mathematics?
Solution: Number of students good in maths = \(\displaystyle \frac{{72}}{{100}}\times \,25\)
= \(\displaystyle \frac{{72}}{4}\)
= 18
To find the number of students that are not good in mathematics we will subtract 18 from 25.
25 - 18 = 7
So, 8 students are not good in mathematics.
Q4. 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 total number of matches be \(\displaystyle x\)
So, 40% of \(\displaystyle x\) will be equal to 10
40% of \(\displaystyle x\) = 10
\(\displaystyle \frac{{40}}{{100}}\times \,x\) = 10
\(\displaystyle \frac{{4}}{{10}}\times \,x\) = 10
x = 10 \(\displaystyle \times \) \(\displaystyle \frac{{10}}{4}\)
= \(\displaystyle \frac{{100}}{4}\)
= 25
So, the number of matches they play in all is 25.
Q5. If Chameli had ₹ 600 left after spending 75% of her money, how much did she have in the beginning?
Solution: Let the money she had be \(\displaystyle x\)
she spend money = 75% 0f \(\displaystyle x\)
= \(\displaystyle \frac{{75}}{{100}}\) of \(\displaystyle x\)
the money she had left = 600
so the required equation is \(\displaystyle x\) - \(\displaystyle \frac{{75}}{{100}}\) \(\displaystyle \times \) \(\displaystyle x\) = 600
\(\displaystyle x\) - \(\displaystyle \frac{{75}}{{100}}\,x\,\) = 600
\(\displaystyle \frac{{100x\,-75x}}{{100}}\) = 600
25\(\displaystyle x\) = 600\(\displaystyle \times \) 100
25\(\displaystyle x\) = 60000
\(\displaystyle x\) = \(\displaystyle \frac{{60000}}{{25}}\)
\(\displaystyle x\) = \(\displaystyle \frac{{12000}}{5}\)
\(\displaystyle x\) = 2400
Hence, Chameli had Rs 2400 in the beginning.
Class 8 Maths Chapter 8 Comparing Quantities Exercise 8.1 Solution of NCERT
Q6. If 60% of people in a city like a 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: percent of people like cricket = 60%
percent of people like football = 30%
So,the percent of people like other games = 100 - (60 + 30)
= 100 - 90
= 10
Hence, 10% people like other games.
Number of people like Cricket = 60% of 50,00,000
= \(\displaystyle \frac{{60}}{{100}}\,\,\times \,5000000\)
= 60 \(\displaystyle \times \) 50000
= 30,00,000
So, the number of people like Cricket is 30,00,000 ( 30 lakhs).
Number of people like Football = 30% of 50,00,000
= \(\displaystyle \frac{{30}}{{100}}\,\,\times \,5000000\)
= 30 \(\displaystyle \times \) 50000
= 15,00,000
So, the number of people like Football is 15,00,000 ( 15 lakhs).
Number of people like other games = 10% of 50,00,000
= \(\displaystyle \frac{{10}}{{100}}\,\,\times \,5000000\)
= 10 \(\displaystyle \times \) 50000
= 5,00,000
So, the number of people like other games = 5,00,000( 5 lakhs).
Class 8 Maths Chapter 8 Comparing Quantities :
- NCERT Class 8 Maths Chapter 8 Comparing Quantities Exercise 8.1
- NCERT Class 8 Maths Chapter 8 Comparing Quantities Exercise 8.2
- NCERT Class 8 Maths Chapter 8 Comparing Quantities Exercise 8.3