Question

The difference between S.I and C.I on a certain sum of 3 years at 8%p.a. is Rs.157.50.find the sum.

Answer 1

The difference between S.I and C.I on a certain sum of 3 years at 8%p.a. is Rs.157.50.find the sum.?

solution :
           There is a mistake in ur question .

It should be difference between C.I and S.I instead of S.I and C.I because Compound Interest of any amount  is always greater than Simple Interest of the same amount for the same time period.
Given
        C.I - S.I = 157.5 .............. (1)
       time = 3 years
       rate of interest =  8% per annum
    let the sum be  = x
therefore ,
         S.I = principal *R*T/100
             = x*8*3/100h8
             =24x/100
             S.I= 0.24x .................. (2)
     Amount = x (1+8/100)³
                 = x (100+8/100)³
                 =x(108/100)³
                 = x(1.25)
               amount  =1.25x
C.I = amount - sum
       = 1.25x - x
     C.I = 0.25 x ......................... (3)
Using 2nd and 3rd in 1st equation , we get
     0.25 x  - 0.24x = 157.5
       .1 x = 157.5
     or x/10 = 157.5
       x= 1575
hence the sum is 1575 rupees

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