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

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