## Important Percentage Formulas

Percentage is a number or ratio expressed as a fraction of 100. Percent is denoted by the symbol %.

For example, x percent is denoted by x%

x% = x/100,

e.g.: 25%=25/100=1/4

1) To express x/y as a percent, we have x/y=(x/y×100)%

Example: 1/4=(1/4×100)%=25%

2) If the price of a commodity increases by R%, the reduction in consumption so as not to increase the expenditure = [R/(100+R)×100]%

3) If the price of a commodity decreases by R%, the increase in consumption so as not to decrease the expenditure = [R/(100−R)×100]%

4) If the population of a town = P and it increases at the rate of R% per annum, then Population after n years = P(1+R/100)^n

5) If the population of a town = P and it increases at the rate of R% per annum, then Population before n years = P/(1+R/100)^n

6) If the present value of a machine = P and it depreciates at the rate of R% per annum, Then Value of the machine after n years = P(1−R/100)^n

7) If the present value of a machine = P and it depreciates at the rate of R% per annum, Then Value of the machine before n years = P/(1−R/100)^n