# Formulas To Solve Percentages Questions

## Formulas for Percentages & Definitions

In mathematics, a percentage is a number or ratio expressed as a fraction whose denominator (bottom) is 100.
Thus, x percent means x hundredths, written as x%.
We express x% as a fraction as x/100 ## Video on Percentages

Formulas and Explanation of Percentage are present in this Video

## Percentages Formulas & Basic Concept

• To calculate a % of b = (a * b)/100
• To find what percentage of a is b = b/a × 100
• To calculate percentage change in value
Percentage change = [change/(initial value)] * 100
• Percentage Increase/Decrease
Percentage increase = (R/(100 + R) * 100)%
Percentage decrease = (R/(100 – R) * 100)%
• Successive Percentage Change
If there are successive percentage increases of a % and b%, the effective percentage increase is: {(a + b + (ab/100)}%
• Results on population
Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:
1.Population after n years = P (1 +R/100)n
2. Population n years ago = P/(1 +R/100)n
• Results on Depreciation:
Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:
1.  Value of the machine after n years = P (1 – R/100)n
2.  Value of the machine n years ago = P/ (1 – R/100)n
3.  If A is R% more than B, then B is less than A by [R/(100 + R) * 100]%
4.  If A is R% less than B, then B is more than A by [R/(100 – R) * 100]%