Aptitude::Percentage
Important Formulas 
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 = 15.
To express a/b as a percent: We have, a/b = (a/b * 100)%.
Thus, 1/4 = (1/4 * 100)% = 25%.
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) * 100]%
If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:
[R/(100R) * 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]%.
