Important Formula: Percentages

## 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.

 Percentage formula = (Value/Total value) × 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

The document Important Formula: Percentages | CSAT Preparation - UPSC is a part of the UPSC Course CSAT Preparation.
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## FAQs on Important Formula: Percentages - CSAT Preparation - UPSC

 1. What is the formula for calculating percentages?
Ans. The formula for calculating percentages is: (Part/Whole) x 100.
 2. How can percentages be used in everyday life?
Ans. Percentages are commonly used in everyday life for calculating discounts, taxes, tips, grades, and analyzing data.
 3. What is the difference between a percentage increase and a percentage decrease?
Ans. A percentage increase represents an increase in value compared to the original value, while a percentage decrease represents a decrease in value compared to the original value.
 4. How can percentages be converted into fractions and decimals?
Ans. To convert a percentage into a fraction, simply divide the percentage by 100. To convert a percentage into a decimal, divide the percentage by 100 or move the decimal point two places to the left.
 5. How can percentages be used in financial calculations?
Ans. Percentages are commonly used in financial calculations such as calculating interest rates, investment returns, and loan payments.

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