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)