## What do you mean by Percentage?

• Percent is derived from the Latin word ‘per centum’ which means ‘per hundred.
• A percentage is a way of comparing quantities.
• Percentages are basically numerators of fractions with denominator 100.
• Percent is represented by the symbol – ‘%’.

Ex- 1% means 1 out of 100 or one-hundredths.

1% = 1/100 = 0.01

### Interpreting Percentages

Example – What do you mean by this statement.

Let say – “Raj saves 25% of his income.

Interpretation – It means 25 parts out of 100, or it means Raj is saving 25 rupees out of every 100 rupees that he earns.

### Important Formulas

1. % Change – (Increase or decrease)

℅change = [(Final value – Initial Value)/ Initial Value] × 100

• Remember Percentage change is always calculated wrt the initial value. So, take the initial value as the reference value for finding %change.
• Note- Always take ‘+’ for an increase and ‘-‘ for a decrease.

2. If the price of an article increases or decreases by ‘x℅’, then the reduction in consumption, and expenditure remaining same.

[(100 × x)/(100 + x)] ℅

3. If the price of an article decreases by ‘x℅’, then the reduction in consumption, and expenditure remaining same

[(100 × x)/(100 – x)] ℅