Question

A sum of money is invested at C.I. payable annually. The interest in two successive years is 225 and 240. Find the rate of interest and original sum

Answer 1

Amount after 1 year = A  = P (1 +r/100)^1 = P (1 + r/100)
      Interest = P r /100 = 225 
      => P r = 22,500      --- equation 1

Amount after 2 years = B = P(1+r/100)^2  = A (1 + r/100)
Interest during 2nd year =  B - A = A r /100 = 240
                      A r = 24 000      -- equation 2
   Hence    P (1 + r/100) r = 24 000,        now substitute Pr from equation 1
                  (1 + r/100 ) = 24 000 / 22 500
                      r /100 = 0.0667
                      r = 6.67 % per annum

                 P = 22 500 / r = Rs 3, 375 

    amount after 1 year = Rs 3 600
   amount after 2 nd  year = Rs 3, 840

Answer 2

diff. in interest=PXR/100
15=225XR/100
R=1500/225=6.67%

PR/100=225
PR=22500
P=22500X3/20=3375

So the original sum is 3375