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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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