Page 87 - ICSE Math 8

Increase in value
Increase in percentage = Original value × 100% Try These

Decrease in value 1. A number when decreased
Decrease in percentage = Original value × 100% by 17% becomes 531.2. Find

Increase in percentage the original number.
So, Increase in value = 100% × Original value 2. A number when increased
by 19% becomes 178.5. Find
∴ New value = Original value + Increase in value the original number.
Increase in percentage
= Original value + 100% × Original value

= Original value (1 + percentage as a fraction)
Similarly, new value in the case of decrease in percentage is given by:
New value = Original value (1 – percentage as a fraction)
 100 x− 
If any given number is decreased by x%, New number =   × Original number
 100 
 100 x+ 
If any given number is increased by x%, New number =   × Original number
 100 
Example 8: Aman spent 3% of his salary to buy some books and 8% of the remaining salary on groceries.
If he is left with ` 40,158, find his salary.
Solution: Let the salary of Aman be x.
97x
Amount left after he buys books = (100 – 3)% of x = 97% of x =
100
Amount left after 8% of remaining amount is spent on groceries = (100 – 8)% of 97x
100
97x 92 97x
= 92% of = ×
100 100 100
According to the question,
92 97x 40,158 × 100 × 100
× = 40,158 ⇒ x = = ` 45,000
100 100 92 × 97
Example 9: If the price of sugar is increased by 30%, by how much per cent must a man decrease his
consumption of sugar so as to keep his expenditure on sugar unaltered?
Solution: Let the original price of sugar be ` 100.
Present price of sugar = ` (100 + 30) = ` 130
So, to keep the expenditure unaltered, i.e., same as earlier of ` 100 present consumption should
be decreased by ` 130 – ` 100 = ` 30 on ` 130.
On ` 130, the consumption should be decreased by ` 30
` 30
On ` 1, the consumption should be decreased by `
130
` 30 1
On ` 100, the consumption should be decreased by ` 130 × 100 = 23 13 %

EXERCISE 7.2

1. Determine the percentage change for the following numbers.

(a) 60 to 75 (b) 75 to 60 (c) 5.25 to 7.875
2. A number when decreased by 12.5% becomes 525. Find the original number.

75