# Important Formulae of Percentage | KEEN LMS

Percentage is an important topic for every competitive exams including SSC, CGL, CGLE, CPO, MTS, IBPS PO, Clerk, Railways and other centre and State government entrance. Good understanding of percentage helps in understanding other topics such as Profit & Loss, Simple Interest, Compound Interest and Data Interpretation where the questions are based on the concept of percentages.

## What is Percentage?

Percent represents part-to-whole relationship and is mathematically written as “out of one hundred” or “per 100” where “Part-to-whole” is defined as the mathematical expression for how many parts you have out of the whole thing. So, when we say 50%, we actually mean to say 50 per 100 a percentage can also be defined as a fraction where the denominator is always 100 and the numerator is called rate percent. Hence, 27% = 27⁄100 15% = 15⁄100

## Important Formulae

- Percentage increase = ( Increase / Original value ) x 100
- Percentage decrease = ( Decrease / Original value ) x 100
- If the price of a commodity increases by r %, then the reduction in consumption so as not to increase the expenditure

[^{r}⁄_{(100+r)}x 100]% - To calculate Increase in consumption when price of a commodity is decreased by r % without decreasing the expenditure, use the formula

[^{r}⁄_{(100-r)}x 100]% - If A’s income is r % more than B’s income, then B’s income is less than A’s income by [
^{r}⁄_{(100+r)}x 100]% - If A’s income is r % less than B’s income, then B’s income is more than A’s income by [
^{r}⁄_{(100-r)}x 100]% - Let the population of a town be P and it increases at the rate of r % per annum, then
- To calculate the Population of the town after n years, use the formula P(1+
^{r}⁄_{100})^{n} - To calculate the Population of the town n years ago, use the formula
^{P}⁄(_{1 + r⁄100)n}

- To calculate the Population of the town after n years, use the formula P(1+

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