# Percentage Important formulas:

Percentage Important formulas:
1.Concept of Percentage:
By a certain percent, we mean that many hundredths.
Thus, x percent means x hundredths, written as x%.
To express x% as a fraction: We have, x% = x/100 .

Thus,

20% = 20/100 = 1/5 .
To express a/b as a percent: We have, a/b = (a/b x 100) %.

Thus,

1/4 = (1/4 x 100)% = 25%.
2.Percentage Increase/Decrease:
If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:

[R /(100 + R) x 100] %
If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

[R/(100 – R) x 100] %
3.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

4.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) x 100] %
4. If A is R% less than B, then B is more than A by [R/(100 – R) x 100] %