Question

A sum of Rs. $44,200$ is divided between John and Smith, $12$ years and $14$ years old respectively, in such a way that if their portions be invested at $10$ percent per annum compound interest, they will receive equal amount on reaching $16$ years of age.

What is the share of each out of Rs. $44,200$

Answer 1

Age of John $=12years$

Age of Smith$=14years$

Let John get $=xRs.$

$\Rightarrow$ smith get$=(44200-x)Rs.$

When John will be $16$ years old, he will

have money = $x(1+\frac{10}{100}{)}^4$

$=x{\left(\frac{11}{10}\right)}^4$

When Smith will be $16$ years old, he will have

money = $(44200-x){[1+\frac{10}{100}]}^2$

$=(44200-x){\left(\frac{11}{10}\right)}^2$

As both will have same amount

$\Rightarrow (44200-x){\left(\frac{11}{10}\right)}^2=x{\left(\frac{11}{10}\right)}^2$

$\Rightarrow 44200-x=\frac{121x}{100}$

$\Rightarrow 44200=\frac{121}{100}x+x=\frac{221}{100}x$

$\Rightarrow x=\frac{44200\times 100}{221}=20000$ Rs.

$\Rightarrow$ John was given amount $=20000Rs.$

and Smith get $=44200-20000$

$=24200Rs.$