Question

    A farmer wants to divide Rs 1,22,000 between his sons ,

    who are 18 and 20 years old respectively, in such a way that the sum divided at the rate of 20% per annum, compounded annually, will give the same amount to each of them when they attain the age of 22 years. How should he divide the sum?
    A Rs 57,000, Rs 65,000 Correct Answer Incorrect Answer
    B Rs 66,000, Rs 56,000 Correct Answer Incorrect Answer
    C Rs 50,000, Rs 72,000 Correct Answer Incorrect Answer
    D Rs 45,000, Rs 77,000 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the farmer give Rs x to the 18 years old son and the remaining Rs (1,22,000 - x) to his 20 years old son. Now,  [x(1+(20/100))]4 = (1,22,000 - x) (1+(20/100))2 ⇒ [x(120/100)]2 = (1,22,000 - x)   ⇒ [x(6/5)]2 = (1,22,000 - x)   ⇒ x(36/25) = (1,22,000 - x) ⇒ ((36/25)+1) x = 1,22,000 ⇒ ((36 + 25)/25) x = 1,22,000 ⇒ x = (1,22,000 × 25)/61 = 50,000 ∴ x = Rs 50,000 For 18 years old son = Rs 50,000 For 20 years old son = Rs 72,000 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+(20/100))(20-18) = (6/5)2 = 36/25 So for 18 years old(1st child)  , sum = [25/(36+25)] × 122000 = (25/61) × 122000 = 50000 & for 20 years old(2nd child)  , sum = [36/(36+25)] × 122000 = (36/61) × 122000 = 72000

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