# Aptitude - Percentage

### Exercise :: 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 = 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

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 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)

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 n 100

2. Population n years ago = P 1 + R n 100

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 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)

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