Percentage - Important Points
What is percentage
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". A percentage is a dimensionless number (pure number).
For example: If a student scores 96 marks in math out of 100, his percentage score is 96. But, if he scores 96 marks in the subject, we cannot say that he has scored 96% marks unless we know the total marks (base). If you don’t know the base, you can’t calculate the percentage.
How to calculate percentage
a is what % of b = (a/b) X 100
b is what % of a = (b/a) X 100
Example 1: 96 is what % of 100.
Solution: (96/100) X 100 = 96%
Example 2: 96 is what % of 200.
Solution: (96/200) X 100 = 48%
Percentages to Fractions
Percentage to fraction conversion is important to solve the questions quickly. Fraction to percentage table can be obtained by successively dividing both sides by 2 or 3.
Percentage |
Fraction |
Percentage |
Fraction |
100 |
1 |
100 |
1 |
50 |
1/2 |
33.33 |
1/3 |
25 |
1/4 |
16.67 |
1/6 |
12.5 |
1/8 |
11.11 |
1/9 |
6.25 |
1/16 |
20 |
1/5 |
37.5 |
3/8 |
22.22 |
2/9 |
18.75 |
3/16 |
40 |
2/5 |
62.5 |
5/8 |
66.66 |
2/3 |
14.28 |
1/7 |
9.09 |
1/11 |
In the above table, 3/8 is 37.5% (12.5 x 3), 5/8 is 62.5% (12.5 x 5).
Example 3: Calculate 62.5% of 800
Solution: 62.5% of 800 = (5/8) of 800 = 500
Example 4: Calculate 18.18% of 2200.
Solution: 18.18% of 2200 = (2/11) of 2200 = 400
Percentage Increase and Decrease
If there is a% and b% change then the equivalent percent change is [a + b + (ab/100)]
Note: a and b should be taken positive for % increase and negative for % decrease.
Example 5: If A’s salary is first increase by 20% then decreased by 10%, then calculate the net percentage change.
Solution: Net %change = 20 – 10 + (20 x -10)/100 = 8%. (8% increase)
Example 6: If B’s salary is first decrease by 20% then increased by 10%, then calculate the net percentage change.
Solution: Net %change = -20 + 10 + (-20 x 10)/100 = -12%. (12% decrease)
Successive Percentage change
- If there is a% and b% increase then the equivalent percent increase is [a + b + (ab/100)]
- If there is a%, b% and c% increase then the equivalent percent increase is [a + b + c + (ab/100) + (bc/100) + (ac/100) + (abc/100)]
Note: Multiplying factor technique would be more useful in this calculation.
Approximation techniques to calculate percentage values
Calculate the value of 11% of 1234 = (10% + 1%) of 1234 = 123.4 + 12.34 = 135.74
Calculate 36% of 1325 = (40% - 4%) of 1325 = (2/5) of 1325 – (1/25) of 1325
= 530 – 53 = 477.
Calculate 18% of 3250 = (20% – 2%) of 3250
= [(1/5) – (1/50)] of 3250 = [(650 – (65)] = 585.
Change of base in percentage
If A is r % more than B, then B is 100r/(100 + r) % less than B. Again if A is r % less than B, then B is 100r/(100 - r) % more than A.
For example, If A is 20% more than B, then B is (100 X 20)/ (100 + 20) = 16.66% less than A.
For example, If A is 20% less than B, then B is (100 X 20)/ (100 - 20) = 25% more than A.