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?

Answer 1

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.