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
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.
1. % Change – (Increase or decrease)
- 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.
3. If the price of an article decreases by ‘x℅’, then the reduction in consumption, and expenditure remaining same
4. If the population of a town is ‘P’ and the annual increase is x%, then population after ‘t’ years.
5. If the population of a town is ‘P’ and the annual decrease is x%, then population after ‘t’ years.
6. If first value is ‘x%’ more than the 2nd value, then the 2nd value –
% Less than the first value.
7. If the first value is ‘x%’ less than the 2nd value, then the 2nd value –
% more than the first value
8. If a number is first increased by x℅ and then again decreased by x% then the net result will be –
% decrease (always)
9. If a number is first increased by x℅ and then again decreased by y% then the net result will be –
() % decrease or increase, depending upon the sign.
10. If a number is successively increased by x% and y% then the net increase is –
11. If the length of a rectangle is increased by x% and its breadth is increased by y%, then the change in its area –
(if the result is +ve then increase and if -ve then decrease)