Important Formula: Percentages | CSAT Preparation - UPSC PDF Download

Percentage

Percentage basically means a part per hundred. A fraction whose denominator is 100 is called a percentage .

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.

It is represented by % symbol. In all the fractions where the denominator is 100 we remove the denominator and put the % sign. 

Calculating percentage of a number

To calculate the percentage of a number, we need to use a different formula such as:

P% of Number = X

where X is the required percentage.

If we remove the % sign, then we need to express the above formulas as;

P/100 * Number = X

Let us understand with help of some examples.

Example: Calculate 10% of 80.
Solution: Let 10% of 80 = X

10/100 * 80 = X

X = 8

Example: The number 450 is what percentage of 1200?
Solution:  = (450/1200) × 100

By simplifying the fraction, we get

= (3/8) × 100 

= 0.375 × 100

= 37.5%

So, the number 450 is 37.5% of 1200.

Example: Convert 0.32 to percentage.
Solution: Multiplying 0.32 by 100, we get 0.32 × 100 = 32% as the answer.

Example: Convert the fraction 23/25 to percentage.
Solution: Converting 23/25 to a decimal value, we get 0.92. 

So, 0.92 × 100 = 92% is the answer.

Percentage Increase and Decrease

(i) Percentage Increase

The percentage increase is equal to the subtraction of the original number from a new number, divided by the original number and multiplied by 100.

% increase = [(New number – Original number)/Original number] x 100

where, increase in number = New number – original number

(ii) Percentage Decrease

Similarly, a percentage decrease is equal to the subtraction of a new number from the original number, divided by the original number and multiplied by 100. 

% decrease = [(Original number – New number)/Original number] x 100

Where decrease in number = Original number – New number