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    Question

    A farmer wants to divide Rs 2,81,800 between his sons ,

    who are 17 and 19 years old respectively, in such a way that the sum divided at the rate of 12% per annum, compounded annually, will give the same amount to each of them when they attain the age of 21 years. How should he divide the sum?
    A Rs 57,000, Rs 124,800 Correct Answer Incorrect Answer
    B Rs 66,000, Rs 215,800 Correct Answer Incorrect Answer
    C Rs 50,000, Rs 231,000 Correct Answer Incorrect Answer
    D Rs 45,000, Rs 236,800 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the farmer give Rs x to the 17 years old son & The remaining Rs (2,81,800 - x) to his 19 years old son. Now, 〖x(1+12/100)〗^4 = (2,81,800 - x) (1+12/100)^2 ⇒〖x(112/100)〗^2 = (2,81,800 - x) ⇒ 〖x(28/25)〗^2= (2,81,800 - x) ⇒ x(784/625) = (2,81,800 - x) ⇒ (784/625+1) x = 2,81,800 ⇒ ((784 + 625)/625) x = 2,81,800 ⇒ x = (2,81,800× 625)/1409 = 1,25,000 ∴ x = Rs 1,25,000 For 17 years old son = Rs 1,25,000 For 19 years old son = Rs 1,56,800 Alternate shortcut method: They will get the sum in 2nd to 1st child in the ratio of = (1+R/100)^(difference between their age)=(1+12/100)^(19-17) =(28/25)^2=784/625 So for 17 years old (1st child) , sum = 625/(784+625)×281800=625/1409×281800=125000 & for 19 years old (2nd child) , sum =784/(784+625)×281800=784/1409×281800=156800

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