Solution

Hemant invested Rs. ‘y’ at the rate of (r+2)% per annum on simple interest and after four years Rs. 27520 was obtained as an interest.

y x (r+2)% x 4 = 27520

y x (r+2) x 4 = 2752000

y x (r+2) = 688000

y = 688000/(r+2)    Eq.(i)

If Rs. (y+2500) was invested at the rate of ‘r’% per annum compounded annually and after two years Rs. 16560 was obtained as an interest.

(y+2500)[{(100+r)/100}^2 - 1] = 16560 

Put Eq.(i) in the above equation.

(688000/(r+2)+2500)[{(100+r)/100}^2 - 1] = 16560 

5r^3+2386r^2−54000r−662400=0

(r−30) (5r^2+2536r+22080)=0

There are three values of ‘r’. But two of them are negative and not possible.

So the value of ‘r’ = 30.