PERCENTAGES

       By a certain percent, we mean that many hundredths. Thus x  
       per cent means x hundredths written as x%.   
                            So x% = x/100.
         EXAMPLE:                     1.20% = 20/100 = 1/5
                     2.48% = 48/100 =  12/25

            To express a/b as a percent ,we have             a/b=(a/b*100)%
                
                           Thus 1/4=(1/4*100)%=25%
                                    0.6=6/10=(3/5*100)%=60%
               If the price of commodity increases by r%,then the reduction in consumption                               
       so as not to increase the expenditure is given as follows
                			[r/(100+r)*100]%	  
                        
              If the price of commodity decreased by r%,then the increase in consumption                               
       so as not to decrease the expenditure is given as follows
                			[r/(100-r)*100]%                  
            RESULT ON POPULATION:
                           Let the population of a town be P now and suppose it increases at the 
         rate  R% per annum then
i)Population after n years = P[1+(R/100)]n
ii) Population  n years ago= P/[1+(R/100)]n           RESULT ON DEPRECIATION:
                             Let the present value of a machine be P. Suppose it depriciates at the  
            rate of R% per annum, then 
i)Value of machine after n years = P[1-(R/100)]n
ii)Value of machine after n years = P/[1-(R/100)]n     IMPORTANT
         i)  If  A is R% more than B,then B is less than A by [(R/(100+R))*100]%
ii)If  A is R% less  than B,then B is more  than A by [(R/(100-R))*100]%