A man wants to invest Rs. 16176 in a fixed deposit for his two daughters whose ages are 12 years and 16 years in such a way that, they will get equal amount at an age at 120 years at the rate of 33`(1)/(3)` % per annum compounded annually. Find the share of younger daughter?

Younger daughterElder Daughter (Maturity date of 108 years104 Years Fixed deposit) = (Let, principal) = Rs. cRs. B After 120 years they will get equal amount C (1+1/3)^108=B (1+1/3)^104 C (4/3)^108=B (4/3)^104 C (4/3)^4=B C/B =81/256 Therefore, the sum of 16,176 is invested in a ratio of 81:256 between these two. ∴ Share of younger daughter = 16176/(81+256) × 81 = 16176/337 × 81 = 3,888 ixambee Approach = Rate = 331/3 % = 1/3 The division of sum is in Younger daughterElder Daughter If difference in ages is 1 years 3 4 If difference in ages is 2 years 916 If difference in ages is 3 years 2764 If difference in ages is 4 years 81256 Therefore, The sum is distributed in the ratio of 81 : 256, as the difference in ages is 4 years. ∴ Share of younger daughter = 16176/(81+256) × 81 = 16176/337 × 81 = 3,888