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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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