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Question
A sum of Rs.16820 is to be divided between two girls A and B, 27 and 25 years old respectively, in such a way that, if their portions be invested at 5% per annum compound interest payable annually, they will receive equal amounts on reaching 40 years of age. What is the share of each in the original sum of money?
Solution
Let the share of A be Rs. x.
Then, the share of B = Rs. (16820 - x)
For A : P =Rs.x, r = 5% and n = (40 - 27) years = 13 years
∴ A = `"P"(1 + "r"/100)^"n"`
= Rs.`x(1 + 5/100)^13`
= Rs.`x(21/20)^13`
For B : P = Rs. (16820 - x), r = 5% and n = (40 - 25) years = 15 years
∴ A = `"P"(1 + "r"/100)^"n"`
= Rs.`(16820 - x)(1 + 5/100)^15`
= Rs.`(16820 - x)(21/20)^15`
Given; both receive equal sums on reaching the age of 40 years.
∴ `x(21/20)^13`
= `(16820 - x)(21/20)^15`
⇒ x = `(16820 - x) xx (21/20)^2`
⇒ x = Rs.8820
⇒ 16820 - x
= 16820 - 8820
= 8000
∴ Share of A = Rs.8820 and Share of B = Rs.8000.
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