A man wants to invest Rs 20,220 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?

Solution

For younger son Let the principal be x Time = 120 – 12 = 108 years Rate = 100/3 % For elder son Let the principal be Rs (20220 – x) Time = 120 – 16 = 104 years Rate = 100/3 % Amount of younger = Amount of elder x (1 + r/100)¹⁰⁸ = (20220 – x) (1 + r/100)¹⁰⁴ x (1 + 100/300)¹⁰⁸ = (20220 – x) (1 + 100/300)¹⁰⁴ [x/(20220 – x)] = (4/3)¹⁰⁴/(4/3)¹⁰⁸ [x/(20220 – x)] = 1/(4/3)⁴ [x/(20220 – x)] = 81/256 337x = 1637820 x = 4860 Alternate method: y/x =(4/3)^(difference)=(4/3)⁴= 256/81 81/337 × 20,220 = 4860