Rs. 260200 is divided between Ram and Shyam so that the amount that Ram receives in 3 years is the same as that Shyam receives in 6 years. If the interest is compounded annually at the rate of 4% per annum then Ram's share is = ?

Answer: Option B

Let Ram get Rs. x and
Shyam get Rs. (260200 - x)
Then Amount get by Ram after 3 years
$$\text{ = }x\times {\left(1+\frac{4}{100}\right)}^3$$
and Amount get by Shyam after 6 years
$$=\left(260200-x\right)\times {\left(1+\frac{4}{100}\right)}^6$$
But both get equal amount
$$\therefore x\times {\left(1+\frac{4}{100}\right)}^3=\left(260200-x\right)\times$$       $${\left(1+\frac{4}{100}\right)}^6$$
$$\begin{array}{rl}& \Rightarrow \frac{x}{2600200-x}=\frac{17576}{15625}\\ & \Rightarrow 15625x=4573275200-17576x\\ & \Rightarrow 33201x=4573275200\\ & \Rightarrow x=137745.022\end{array}$$
So, Ram will get Rs. 137745.022