Sunday, July 14, 2013

11:01 AM
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 two-step 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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