Question

A man leaves his estate to his wife and two sons. If the wife receives $\dfrac{2}{3}$ of the estate and each son receives $\dfrac{1}{2}$ of the remainder, find the value of the estate in rupees if each son receives Rs 40000 as his share.
(a) 120000
(b) 200000
(c) 160000
(d) 240000

Answer 1

Hint: Here, first we will assume the entire value of the estate as x rupees. Then, we find the share of the remaining estate by subtracting the wife share from the total estate value. Then, we will find the value of each son's share by dividing the remaining share by 2. Then, we will equate the calculated expression to the value of Rs 40000 and find the total value of estate in rupees.

Complete step-by-step answer:
In this question, we are supposed to find the total value of the estate in rupees.
For that, we assume the total value of the estate will be x rupees.
Then, according to the condition given in the question which says that $\dfrac{2}{3}$ part of the estate is given to his wife.
So, the part of the estate given to the wife is Rs $\dfrac{2}{3}x$.
Now, we will find the remaining part of the estate after giving the wife's share by subtracting the wife share from the total estate value.
So, remaining part after giving wife’s share is:
$\begin{align}
  & \left( x-\dfrac{2}{3}x \right)=\left( \dfrac{3x-2x}{3} \right) \\
 & \Rightarrow \dfrac{x}{3} \\
\end{align}$
So, the remaining amount of estate after giving the wife's share is Rs $\dfrac{x}{3}$.
Now, by applying the second condition that each of the two sons get the equal share from the remaining part.
Then, the share of each son is half of the remaining amount of the estate after giving the wife's share.
So, each son share is:
$\dfrac{1}{2}\times \dfrac{x}{3}=\dfrac{x}{6}$
So, the amount received by each son is Rs $\dfrac{x}{6}$.
The above expression value is given in the question as the amount of the estate received by the son is Rs 40000. So, by equating above equation to 40000:
$\begin{align}
  & \dfrac{x}{6}=40000 \\
 & \Rightarrow x=240000 \\
\end{align}$
So, the total value of the estate is Rs 240000.
Hence, option (d) is correct.

Note: The most common mistake you will do in finding the value of each son share as you will consider each son share as $\dfrac{1}{2}x$ which leads to the value of the total estate as
$\begin{align}
  & \dfrac{1}{2}x=40000 \\
 & \Rightarrow x=80000 \\
\end{align}$
From the above consideration the answer will be wrong as in the question it is clearly mentioned that each son's share is $\dfrac{1}{2}$ of the remaining value after giving his wife's share. So, read carefully before calculating each person’s share from the total estate value.