Class 8 NCERT Solutions Chapter 8 Comparing Quantities Exercise 8.1 (original) (raw)

Last Updated : 12 Sep, 2024

In Chapter 8: Comparing Quantities students learn how to compare different values and express relationships between them in various forms such as ratios, percentages, and fractions. This chapter also introduces key concepts like profit and loss, simple interest, and discount helping students develop a strong understanding of how quantities are compared in real-life situations. Exercise 8.1 is designed to test the student's grasp of these foundational concepts.

What is Comparing Quantities?

Comparing Quantities involves determining how one value relates to another often by using tools like ratios, percentages or fractions. For example: comparing quantities helps in understanding how much more or less one item is in comparison to the other. It is useful in various everyday contexts such as determining price discounts, calculating profit/loss, or understanding growth rates.

**Question 1: 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.

(b) 5 m to 10 km (c) 50 paise to ₹ 5

**Solution:

(a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour

Ratio = Speed of Cycle : Speed of Scooter

= 15 km per hour : 30 km per hour

= 15/30 = 1/2

So, the ratio is 1 : 2

(b) 5 m to 10 km

First of all, the units of both quantities must be same

So, Convert 10 km into m

Since 1 km = 1000 m

Hence, 10 km = 10,000 m

Ratio = 5 m : 10,000 m

= 5/10000 = 1/2000

So, the ratio is 1 : 2000

(c) 50 paise to ₹ 5

First of all, the units of both quantities must be same

Convert ₹ 5 into paise

Since ₹ 1 = 100 paise

Hence, ₹ 5 = 500 paise

Ratio = 50 paise : 500 paise

= 50/500 = 1/10

So, the ratio is 1 : 10

**Question 2: Convert the following ratios to percentages.

(a) 3 : 4 (b) 2 : 3

**Solution:

In order to convert ratios to the percentage, we must multiply it with 100

(a) 3 : 4

3 : 4 = (3/4) X 100 = 75%

(b) 2 : 3

2 : 3 = (2/3) X 100 = 66.66% or 67% (approx)

**Question 3: 72% of 25 students are good in mathematics. How many are not good in mathematics?

**Solution:

**Method 1:

Total students = 25

72% student are good in mathematics, converting it to numbers

Number of students good in mathematics = 72% of 25

= (72/100) X 25

= 18

So number of students who are not good in mathematics = 25 - 18 = 7

So, 7 students are there who don't like mathematics.

**Method 2:

It is given that72% of 25 students are good in mathematics

So the percentage of people who are not good in mathematics 100% - 72% = 28%

Number of people who are not good in mathematics = 28% of 25 = (28/100) X 25 = 7

So, 7 students are there who don't like 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:

**Method 1:

Let us assume that the team played 100 matches and the winning percentage is 40

So, we can say the team won 40 matches out of 100

Also, they won 1 match out of 100/40 matches

Hence, 10 matches were won out of (100/40) X 10 = 25

So, the football team played 25 matches in all.

**Method 2:

Let us assume the football team played a total of x matches

The winning percentage is 40% and they won 10 matches

So, we can say

40% of x = 10

(40/100). x = 10

Hence, x = 25

So, the football team played 25 matches in all.

**Question 5: If Chameli had ₹ 600 left after spending 75% of her money, how much did she have in the beginning?

**Solution:

**Method 1:

Let us assume that Chameli had ₹ 100 in the beginning

It is given that Chameli had spent 75% of her money

So the money spent by her = 75% of 100 = (75/100) X 100 = ₹75

Hence, money left with her = ₹100 - ₹75 = ₹25

Now,

₹25 are left if she had ₹100 in the beginning

₹1 is left if she had ₹(100/25)

So, ₹600 will be left if she had ₹(100/25) X 600 i.e ₹2400 in the beginning

Hence, Chameli had ₹2400 in the beginning.

**Method 2:

Let us assume Chameli had ₹x in the beginning

After spending 75% of x she had ₹ 600 left

So, (100 - 75)% of x = ₹600

= >(25/100). x = 600

Hence, x = ₹2400

Hence, Chameli had ₹2400 in the beginning.

**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 are 50 lakh, find the exact number who like each type of game.

**Solution:

Total number of people = 50 lakh

60% of people like Cricket

So, the number of people like Cricket = 60% of 50,00,000

= (60/100) X 50,00,000 = 30,00,000

30% of people like Football

So, the number of people like Football = 30% of 50,00,000

= (30/100) X 50,00,000 = 15,00,000

Percentage of people like other games = (100% - 60% - 30%) = 10%

So, the number of people like other games = 10% of 50,00,000

= (10/100) X 50,00,000 = 5,00,000

Hence, 30 lakh people like Cricket, 15 lakh people like Football and 5 lakh people like other games.

Conclusion

Understanding how to compare quantities is a fundamental mathematical skill with the numerous real-life applications from the financial transactions to analyzing data. Chapter 8 of NCERT Class 8 ensures students can use ratios, percentages and fractions effectively to the compare different values. By mastering this, students will be better equipped to deal with the everyday scenarios involving comparisons such as the understanding price increases or interest on savings.