A man wants to invest Rs 40,440 in bank account of his two sons whose age were 12 years and 16 years in such a way that they will get equal amount at age of 120 years @ 33 1/3% per annum compounded annually. Find the share of younger son?

A = P+ (1+ r/100)^n Let the principal for younger son be Rs x Principal for elder son be Rs y Interest to be calculated for Younger son = (120 – 12) = 108 years Elder son = (120 – 16) = 104 years Since, amount will be equally distributed then, ⇒x (1+ 100/300)^108 = y (1+ 100/300)^104 ⇒ x (4/3)^108 = y (4/3)^104 〖⇒(4/3)〗^(108 - 104) = y/x ⇒ y/x = 256/81 ∴ Younger son’s share = 81/337 ×40,440 = Rs 9,720

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