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Percentage- Facts and Formula

  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% =20/100 =1/5; 48% =48/100 =12/25, etc.

    To express a/b as a percent : We have, a/b =((a/b)*100)%.

    Thus, ¼ =[(1/4)*100] = 25%; 0.6 =6/10 =3/5 =[(3/5)*100]% =60%.

  2. If the price of a commodity increases by R%, then the reduction in consumption so asnot to increase the expenditure is [R/(100+R))*100]%. If the price of the commodity decreases by R%,then the increase in consumption so as to decrease the expenditure is [(R/(100-R)*100]%.
  3. Results on Population : Let the population of the town be P now and suppose it increases at the rate of R% per annum, then :
    • Population after nyeras = P [1+(R/100)]^n.
    • Population n years ago = P /[1+(R/100)]^n.
  4. Results on Depreciation : Let the present value of a machine be P. Suppose it depreciates at the rate R% per annum. Then,
    • Value of the machine after n years = P[1-(R/100)]n.
    • Value of the machine n years ago = P/[1-(R/100)]n.
  5. If A is R% more than B, then B is less than A by


    If A is R% less than B , then B is more than A by