Some important Questions Percentage
Example 1
The length of a
rectangle increases by 14% and the breadth by 8%. What is the consequent
percentage increase in area? .
Solution
Let length and
breadth of the rectangle be 1 and b. .
Area of
rectangle = 1b
Length is
increased by 14%. .
1 + 1 x 
(1 + 0.141) =
1.141 .
breadth is
increased by 8%
= b + 8% b
= b + 0.08 b .
(1.08) b .
Area of
rectangle
= 1.141 x 1.08b
= (1.2312) 1b .
Increase in Area
is = 1.2312 1b - 1b .
= 0.2312 1b .
\ percentage increase = 
x 100
23.12% increase.
.
Example 2
If the price of
rice rises by 20% by what percentage should a family reduce the consumption in
order to spend the same amount as before?
Solution
(Price per kg) x (Number of kg consumed) = constant = Amount spent
by the family
Let the initial
price be al and consumption be b1. .
The new price a2
= 
a1 = 1.2 a1
Amount spent is
constant a1b1 = a2b2
a1b1
= (1.2) a1 b2 .
= 83.33%
&⇒ 100 - 83.33 = 16.67%. .
\ Consumption has to be reduced by 16.67%. .
Example 3
The population
of a city increases by 20% every year. If the present population is 4,32,000,
what was the population of the city two years ago? .
Solution
Let the population two years ago be 100. .
Then the
population in the last year and the present year are 120 and 144. .
For two years
144 = 4,32,000
100 = ?
x 100
3000 x 100 =
3,00,000
Two years ago
the population was 3,00,000. .
Example 4
Mohan’s salary
was first increased by 20%, then decreased by 20%. If his present salary is Rs.7200,
then what was his original salary? .
Solution
Let Mohan’s salary be Rs.100. .
When increased
by 20%,
Mohan’s salary =
Rs.120 .
Again when
decreased by 20%, Mohan’s salary
= 120 — 24 = Rs.96.
.
But present
salary is Rs.7,200 .
\ for, 96 → 100
7200 → ?
Required salary is
x 100 i.e Rs.7500.
Example 5
Ajay got 30% of
the maximum marks in a test and failed by 15 marks. Bala got 40% of the maximum
marks in it and got 5 marks more than the pass mark. Find the maximum marks and
also the pass marks. .
Solution
Let the maximum marks be M. .
Method 1:
Ajay’s marks = 
M and Bala’s marks = 
M
Ajay failed by
15 marks and Bala got 5 marks more than the pass marks. .
\ Pass marks = M + 15 = M - 5
20 = 
M
&⇒ M = 200. .
Also pass marks
= 30% of 200 + 15 = 75
Method 2:
Let the pass
marks be P. .
Bala’s marks —
Ajay’s marks
= P + 5 - (P -
15) = 20
M – M = 20
M = 200
