Page 111 - ICSE Math 7

Example 9: Sia’s salary was ` 33,000. After six months, it increased by 10%. After next six months,
it decreased by 10%. Find Sia’s salary at the end of the year.
Solution: Original salary = ` 33,000
 10 
Salary after six months = ` 33,000 1+  [New value = Original value

 100 (1 + percentage as a fraction)]

 33 000 11, × 
= `   = ` 36,300
 10 

 10 
Salary after next six months = ` 36,300 1−  [New value = Original value


100 (1 – percentage as a fraction)]
 36 300 9, × 
= `   = ` 32,670
 10 
Alternatively,
Increase in salary = 10% of ` 33,000

10
= × ` 33,000 = ` 3,300
100
∴ Salary after six months = ` 33,000 + ` 3,300 = ` 36,300
Decrease in salary after next six months = 10% of ` 36,300
10
= × ` 36,300 = ` 3,630
100
∴ Salary at the end of the year = ` 36,300 – ` 3,630 = ` 32,670
Example 10: There was a decrease of 60% in Tarun’s bank account at the end of the year. There were
` 6,080 in his account. What was his balance at the beginning of the year?

Solution: Let the balance at the beginning of the year be ` x.
x – 6,080
Percentage decrease = x × 100%
x – 6,080
⇒ 60% = × 100%
x
60 x – 6,080 3 x – 6,080
⇒ = ⇒ =
100 x 5 x
⇒ 3x = 5x – 30,400 ⇒ 2x = 30,400 ⇒ x = 15,200

Example 11: If x is 30% less than y, find:

(a) x (b) y – x
y y
x 7 7
Solution: (a) x = y – 30% of y (b) As = , therefore x = y
y 10 10
7 10y – 7y
30 7y y – x y – 10 y 10
= y – × y = = =
100 10 y 10 y
3
x 7 10 y 3
∴ = = =
y 10 y 10

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