Page 115 - Maths Skills - 8

Comparing Quantities 113

Let’s Attempt

Example 1: If 33% of a number is 99, Example 2: Amisha gets 99 marks in her exams.
find the number. This amounts to 66% of the total
Solution: Let the number be x. marks. Find the maximum marks.
33% of x = 99 Solution: Let the maximum marks be x
We have 66% of x = 99
⇒ 33 × x = 99
100 ⇒ 66 × x = 99
99 100× 100
⇒ x = = 300 99 100×
33 ⇒ x = = 150
Thus, the number is 300. 66
Hence, the maximum marks is 150.

Example 3: 28% of the students in a school are girls. If the total number of girls in the school is 700, find the
total number of students in the school. Also find the total number of boys in the school.
Solution: Let the total number of students be x.
Total number of girls = 28% of x

According to given condition 28 × x = 700
100
700 100×
⇒ x = = 2500
28
Thus, the total number of students = 2500, and the number of boys in the school = 2500 – 700 = 1800.

Example 4: Suppose a man’s monthly income is ` 60000. He spends 13% of his income on rent, and 62% on
other things. How much money did he save every month?

13
Solution: Expenditure on rent = 13% of ` 60000 = × ` 60000 = ` 7800
100
62
Expenditure on other things = 62% of ` 60000 = × ` 60000 = ` 37200
100
∴ Saving = ` 60000 – ` (7800 + 37200) = ` 15000.

Example 5: Suresh’s income is 25% more than that of Rajesh. By how much per cent is Rajesh’s income less
than Suresh’s income?

Solution: Let Rajesh’s income be ` 100. Then, Suresh’s income will be ` 125.
When Suresh’s income is ` 125, Rajesh’s income is ` 100

100
When Suresh’s income is ` 1, Rajesh’s income is `
125
` 100
When Suresh’s income is ` 100, Rajesh’s income is × ` 100 = ` 80
` 125
Less in income = ` (100 – 80) = ` 20

20
Per cent less = × 100% = 20%
100
Hence, Rajesh’s income is 20% less than that of Suresh.