If a quantity is increased or decreased more than once, you cannot simply add or subtract the percentages.You have to work out each increase or decrease step by step.
Let’s see an example where this important concept is used.
Example:
The population of a town increased by 20% between 1989 and 1995. If the population increased again by 10% from 1995 till 2003, what is the percentage increase in the population between 1989 and 2003?
A)
B)
C)
D)
E)
Solution:
Step 1: This is a twostep percentage change problem. Remember if a measure is increased or decreased more than once, you cannot simply add or subtract the percentages. You have to work out each increase or decrease step by step.
Even though 30% is a very tempting answer, it’s wrong!
Let’s say the original population in 1989 is . Sure we don’t know . However the question wants us to know the percentage increase and therefore it will eventually get canceled.
Since the population increased by 20% between 1989 and 1995, the population at the end of 1995 is
Since the population increased by 10% between 1995 and 2003, the population at the end of 2003 will be (remember you now need to use the population in 1995 as the original value i.e. )
Step 2: % Change in population between 1989 and 2003 =
.
The correct answer is D
In order to solve percentage change problems quickly, it’s a good idea to remember some common percentage change values. The following tables show Percentage Increases and Percentage decreases for some commonly used numbers.
Original value 100: Percentage change  Final values
Percentage Change

10

20

30

40

50

60

70

80

90

100

Increase  Final value

110

120

130

140

150

160

170

180

190

200

Decrease  Final value

90

80

70

60

50

40

30

20

10

0

Original value 50: Percentage change  Final values
Percentage Change

10

20

30

40

50

60

70

80

90

100

Increase  Final value

55

60

65

70

75

80

85

90

95

100

Decrease  Final value

45

40

35

30

25

20

15

10

5

0

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