Percentage is very important topic for aptitude subject. Direct questions are not asked from this topic but you will find use of this topic in almost all question of Data Interpretation (DI), Interest, Profit and Loss, Partnership etc.
We will be discussing concept of percentage and shortcut tricks to solve these type of questions.
Here is the table to convert percentage into number, it will be useful while solving questions if you remember it.
| 1% | 1/100=0.01 | 1/100 |
| 2% | 2/100=0.02 | 1/50 |
| 3% | 3/100=0.03 | 3/100 |
| 4% | 4/100=0.04 | 1/25 |
| 5% | 5/100=0.05 | 1/20 |
| 6% | double of 3% => 0.06 | 3/50 |
| 7% | 7/100=0.07 | 7/100 |
| 8% | double of 4% => 0.08 | 2/25 |
| 9% | 3 times of 3% => 0.09 | 9/100 |
| 10% | 10 times of 1% => .10 | 1/10 |
| 15% | 3 times of 5% => 0.15 | 3/20 |
| 20% | 2 times of 10% => 0.20 | 1/5 |
| 25% | 5 times of 5% => 0.25 | 1/4 |
| 30% | 30/100=0.3 | 3/10 |
| 40% | 40/100=0.4 | 2/5 |
| 50% | 50/100=0.5 | 1/2 |
| 60% | 60/100=0.6 | 3/5 |
| 80% | 80/100=0.8 | 4/5 |
Percentage is calculated on the base of 100 (As per means each, cent means 100)
Example 1. Ram obtained 75 marks in maths in his pre-board exam out of 150. How much percent he obtained?
Explanation:
per 150 he obtained 75 marks
per cent (100) he obtained = (75/150)*100 = 50%
Percentage Change:
In such questions we first need to find out the base value (reference value) with respect to which we have to find out the change.
Example 2. Ram obtained 75 marks in pre-board exam. after re-evaluation 25 marks were increased. Find out the percentage change?
Explanation:
Initially, it was 50% {(75/150)*100}, now also we will be calculating percentage on the base value 150.
So, the change in marks =25
=> change in % = (25/150)*100 = 16.66%
We can cross verify it:
Now the total marks = 75+25 = 100
% = (100/150)*100 = 200/3 = 66.66%
Initially it was 50%,
Now, it is 66.66%
So, Change = 16.66%
A change can be of two types – an increase or a decrease.
Another type of questions:
When a value is changed from initial value to a final value,
% change = (Difference between initial and final value/initial value) X 100
Example 3. If 20 changes to 40, what is the % increase?
Explanation:
% increase = (40-20)/20 X 100 = 100%.
Note:
1. With respect to initial value we have to look for the change, so base value here is initial value.
2. If a value is doubled the percentage increase is 100.
3. If a value is tripled, the percentage change is 200 and so on.
Percentage Difference:
% Difference = (Difference between values/value compared with) X 100.
Example 4. By what percent is 40 more than 30?
Explanation:
% difference = (40-30)/30 X 100 = 33.33%
{Here 40 is compared with 30. So 30 is taken as denominator}
Exampl 5. By what % is 60 more than 30?
Explanation:
% difference = (60-30)/30 X 100 = 100%.
{Here is 60 is compared with 30.}
Hint: To calculate percentage difference the value that occurs after the word “than” in the question can directly be used as the denominator in the formula.