1. 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%.

1. 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 :

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.

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

                        [(R/(100+R))*100]%.

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

                        [(R/(100-R))*100]%.