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Percentage

  1. Concept of Percentage: By a certainpercent, we mean that many hundredths. Thus,xpercent meansxhundredths, written asx%.
    To expressx% 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 afternyears = P 1 + R n
    100
    2. Populationnyears 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 afternyears = P 1 - R n
    100
    2. Value of the machinenyears 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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