In Class 8 Chapter 8 Comparing Quantities Ex 8.1-NCERT, we learn how to compare different quantities using concepts like percentages, ratios, and proportions. This chapter helps us understand how to solve real-life problems involving discounts, profit and loss, simple interest, and other situations where quantities need to be compared.
By applying the principles of comparison, we can better analyze and make decisions in various practical scenarios. Through exercises and examples, we will explore how to use these concepts effectively in everyday life.
Class 8 Chapter 8 Comparing Quantities Ex 8.1-NCERT
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:
(a) Speed of cycle : Speed of Scooter = 15 km per hour : 30 km per hour
=15/30 =1/2
Hence, the ratio = 1 : 2
(b) 5 m to 10 km
= 5 m : 10 × 1000 m [∵ 1 km = 1000 m]
= 5 m : 10000 m
= 1 : 2000
Hence, the ratio = 1 : 2000
(c) 50 paise to ₹ 5
= 50 paise : 5 × 100 paise
= 50 paise : 500 paise
ratio = 1 : 10
Class 8 Chapter 8 Comparing Quantities Ex 8.1-NCERT
Ex 8.1 Class 8 Maths Question 2.
Convert the following ratios to percentages:
(a) 3 : 4
(b) 2 : 3
Solution:
Ex 8.1 Class 8 Maths Question 3.
72% of 25 students are good in mathematics. How many are not good in mathematics?
Solution:
Number of students who are good in mathematics = 72% of 25
Number of students who are not good in mathematics = 25 – 18 = 7
Ex 8.1 Class 8 Maths 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:
Given:
Matches won = 10
Win percentage = 40%
Let the total number of matches be x.
Using the formula:
(10 / x) × 100 = 40
10 / x = 40 / 100
10 / x = 2 / 5
Cross-multiplying:
2x = 50
x = 25
Ex 8.1 Class 8 Maths Question 5.
If Chameli had ₹ 600 left after spending 75% of her money, how much did she have in the beginning?
Solution:
Let the money with Chameli be ₹ 100
Money spent by her = 75% of 100
= 75 /100× 100 = ₹ 75
The money left with her = ₹ 100 – ₹ 75 = ₹ 25
₹ 25 are left with her out of ₹ 100
₹ 1 is left with her out of ₹ 100/25
₹ 600 will be left out of ₹ 100/25 × 600 = ₹ 2400
Hence, she had ₹ 2400 in beginning.
Ex 8.1 Class 8 Maths Question 6.
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:
Total number of people = 50,00,000
Number of people who like cricket = 60% of 50,00,000
= 60/100× 50,00,000
= 30,00,000
Number of people who like football = 30% of 50,00,000
= 30/100× 50,00,000
= 15,00,000
Number of people who like other games = 50,00,000 – (30,00,000 + 15,00,000)
= 50,00,000 – 45,00,000
= 5,00,000
Percentage of the people who like other games = 500000/5000000× 100 = 10%
Hence, 10% of people like other game.
Class 8 Chapter 8 Comparing Quantities Ex 8.1-NCERT
Q1: Find the ratio of the following:
(a) Speed of a cycle 15 km per hour to the speed of a scooter 30 km per hour
Ratio = 15 km/h : 30 km/h
= 15 : 30
= 1 : 2
(b) 5 m to 10 km
First, convert 10 km to meters:
10 km = 10 × 1000 = 10000 m
Now,
Ratio = 5 m : 10000 m
= 5 : 10000
= 1 : 2000
(c) 50 paise to Rs 5
First, convert Rs 5 to paise:
Rs 5 = 5 × 100 = 500 paise
Now,
Ratio = 50 paise : 500 paise
= 50 : 500
= 1 : 10
Q2: Convert the following ratios to percentages.
(a) 3:4
To convert the ratio to percentage:
3 ÷ 4 = 0.75
0.75 × 100 = 75%
Answer: 75%
(b) 2:3
To convert the ratio to percentage:
2 ÷ 3 = 0.666…
0.666… × 100 = 66.67% (or 66⅔%)
Answer: 66⅔%
Q3: 72% of 25 students are good in mathematics. How many are not good in mathematics?
72% of 25 = (72/100) × 25 = 18
Total students = 25
Not good in mathematics = 25 − 18 = 7
Answer: 7 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?
Let the total number of matches be x.
Win percentage = 40%
Matches won = 10
Using the formula:
(10 / x) × 100 = 40
⇒ 10 / x = 40 / 100
⇒ 10 / x = 2 / 5
⇒ 2x = 50
⇒ x = 25
Answer: The team played 25 matches in all.
Q5: If Chameli had Rs 600 left after spending 75% of her money, how much did she have in the beginning?
Let the total money Chameli had in the beginning be x.
She spent 75% of her money, so she had 25% left.
25% of x = 600
(25/100) × x = 600
x = 600 × 100 / 25
x = 2400
Answer: Chameli had Rs 2400 in the beginning.
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