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      Question

      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. 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, then find out the value of ‘r’.
      A 25 Correct Answer Incorrect Answer
      B 30 Correct Answer Incorrect Answer
      C 40 Correct Answer Incorrect Answer
      D 20 Correct Answer Incorrect Answer
      E 35 Correct Answer Incorrect Answer

      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.

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