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    Question

    Divide Rs. 53,285 into two parts such that the amount

    received from first part after 12 years is equal to the amount received from second part after 8 years, if interest rate being `12(1)/(2)` % per annum compounded yearly.
    A Rs. 31,285, Rs. 22,000 Correct Answer Incorrect Answer
    B Rs. 25,000, Rs. 28,285 Correct Answer Incorrect Answer
    C Rs. 32,805, Rs. 20,480 Correct Answer Incorrect Answer
    D Rs. 33595, Rs. 19,690 Correct Answer Incorrect Answer

    Solution

    Let the first part be x and the second part be y The first part after 12 years = x ( 1 + 25/200 )¹² The second part after 8 years = y ( 1 + 25/200 )⁸ As given in the problem these two amounts are equal. So, y ( 1 + 25/200 )⁸ = x ( 1 + 25/200 )¹² Or y/x = (1 + 25/200 )⁴ Or y/x = 6561/4096 We have the x + y = Rs. 53,285 Using the ratio formula, y = 6561/(6561 + 4096) × 53,285 = Rs. 32,805 x = 4096/(6561 + 4096) × 53,285 = Rs. 20,480

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