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?

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