Question

(i) Rs. 16,820 is divided between two persons Mr. X and Mr. Y, 27 and 25 years old respectively; and their money is invested at 5% per annum compound interest in such a way that both receive equal money at the age of 40 years. Find the share of each out of Rs.16,820.

Answer 1

Let the part of money of person X is A, and thge part of money of person Y is B.

X man to the age of 40 years left 13 years, and Y man to the age of 40 years left 15 years.

So, every 13 years person X will have 5% more than its part. The averall money after 13 years will be $A+13*0.05A = 1.65A$

Every 15 years person Y will have 5% more than its part. The averall money after 15 years will be $B+15*0.05B = 1.75B$

At the age of 40, the amount of their money will be the same. It means $1.65A=1.75B$

One more equation is $A+B=16820$

We have equation with 2 unknowns: $\begin{alignedat}{2} 1.65A=1.75B \\ A+B=16820 \end{alignedat}$

So, $A = 16820 - B$,

$1.65(16820-B) = 1.75B$,

$27753 - 1.65B = 1.75B$,

$27753 = 3.4B$,

$B = \cfrac{27753}{3.4}\approx8 162.65$,

$A = 16820 - 8162.65\approx8657.35$.

Answer: the share of person X is Rs. 8657.35. The share of person Y is Rs. 8162.65.