Question

the simple interest on a certain sum for 3 years at 8% per annum is 96 more than the simple interest on the same sum for 2 years at 9% per annum find the sum

Answer 1

let the required sum be rs.x

SI on Rs.x at 8%per annum for 3 years

=Rs.(x×8×3/100)=Rs.6x/25

Si on rs.x at 9%per annum for 2 years

=Rs.(x×9×2/100)=Rs.9x/50


6x/25-9x/50=96

=>12x-9x=96×50

=>3x=96×50

=>x=96×50/3=1600

hence the required sumis Rs.1600

Answer 2

Let The sum be x 

SI                      = P.R.T / 100 
_____________________________________________________________

Case I

Principle             = x
Rate                   = 8 % per annum 
Time                  = 3 years 
SI                       = x . 8 . 3 / 100 
                          = 24 x / 100 
____________________________________________________________ 

Case II 

Principle            = x
Rate                  = 8% per annum 
Time                 = 2 years 
SI                      = x . 9 . 2 / 100 
                         = 18 x / 100 
____________________________________________________________

ATQ 

24x / 100 - 18x / 100  = 96 

(24x - 18x ) / 100         = 96

6x / 100                       = 96

6x                                = 9600 

x                                  = 1600