Wednesday, 8 June 2016


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


If the price of the commodity decreases by R%,then the increase in consumption so as to decrease the      expenditure is



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 :


1.      Population after nyeras = P [1+(R/100)]^n.

2.      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,


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.


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



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