Exercise :: Percentage  Important Formulas
 Percentage  Important Formulas
 Percentage  General Questions

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 = 1 . 100 5 To express a as a percent: We have, a = a x 100 %. b b b Thus, 1 = 1 x 100 % = 25%. 4 4 
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 x 100 % (100 + R) If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:
R x 100 % (100  R) 
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 n 100 2. Population n years ago = P 1 + R n 100 
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 n 100 2. Value of the machine n years ago = P 1  R n 100 3. If A is R% more than B, then B is less than A by R x 100 %. (100 + R) 4. If A is R% less than B, then B is more than A by R x 100 %. (100  R)