Finding Percentage Increase and Decrease


There are 10 children in each group below.



 2 more children join Group A.

The number of children in Group A increases by 2.

Percentage increase =  2
10
× 100%
  =  20%
 There are now 20% more children in Group A than before.



 3 children from Group B leave the group.

The number of children in Group B decreases by 3.

Percentage decrease =  3
10
× 100%
  =  30%
 There are now 30% fewer children in Group B than before.


Percentage increase  =  amount increased
initial quantity
  × 100%

Percentage decrease  =  amount decreased
initial quantity
  × 100%


Word Problem 1

Lisa's salary was raised from $4000 to $4800 per month. What was the percentage increase in her monthly salary?



Percentage increase =  $800
$4000
  × 100%
  = 20%

The percentage increase in her monthly salary was 20%.


Word Problem 2

The price of a chair was reduced from $270 to $189 in a sale. Find the percentage discount on the chair.



Decrease in price =  $270 − $189
  =  $81

Percentage decrease =  $81
$270
  × 100%
  = 30%

The percentage discount on the chair was 30%.


Word Problem 3

Joey had a leaky water bottle that leaked 15 ml of water every 10 minutes. What was the percentage decrease in the water in the bottle 1 hour after the bottle was filled up to 450 ml?



10 minutes  15 ml
1 minute  15
10
 ml
60 minutes  15
10
 ml × 60
 =  90 ml
After 1 hour 90 ml of water had leaked from the bottle.

Percentage decrease =  90
450
 × 100%
  = 20%

The percentage decrease in the water after 1 hour was 20%.


Word Problem 4

Due to some roadworks on the usual route from home to school, Peggy has to take another route to school which is 7% longer. This increase in distance is 126 m. What is the length of the new route?



7%   126m
1%  126
7
 m
 =  18 m
107%  18 m × 107
 =  1926 m

The length of the new route is 1926 m.


Word Problem 5

Sue bought a piece of cloth 140 cm long. After washing it, the cloth shrank by 4% along its length. What is the length of the cloth now?



100% − 4% = 96%
96% of 140 cm =  96
100
 × 140 cm
  = 134.4 cm

The length of the cloth is 134.4 cm now.