Question

A man has divided his total money in such a way that half of it goes to his wife, \[\dfrac{2}{3}rd\] of the remaining among his three sons equally and rest among his four daughters equally. If each daughter gets Rs. 20,000, how much will each son get.

(a). Rs.53,333.33
(b). Rs.53000.14
(c ). Rs.45333.33
(d). Rs.52000.44

Answer 1

- Hint: We will solve this question using basic mathematics techniques. We will assume the total money the man has, to be a number and then we would proceed to do further calculations according to the question's requirement to get the answer.

Complete step-by-step solution -

A man has divided his total money in such a way that half of it goes to his wife, \[\dfrac{2}{3}rd\] of the remaining among his three sons equally and rest among his four daughters equally. If each daughter gets Rs. 20,000.
We have to calculate the amount of money which each son gets.
Let the total money of the man be \[100x\].
Given that the share of the wife is half of the total money.
So, the share of the wife will be \[\dfrac{100x}{2}\] i.e. \[50x\].
Now the remaining money is \[50x\].
Now the share of his sons combined is \[\dfrac{2}{3}rd\] of the total left money.
So, the share of his sons is,
\[\dfrac{2}{3}\left( 50x \right)\].
Hence, the share of the sons is 33.34x.
Now the share of all daughter after the share of the sons is removed is 16.66x
As there are 4 daughters.
Therefore, the share of one daughter will be,
\[\begin{align}
  & \dfrac{16.66}{4} \\
 & \Rightarrow 4.165x \\
\end{align}\]
Now we are given that the share of one daughter is Rs 20,000.
Therefore, we have,
\[\begin{align}
  & 4.165x=20000 \\
 & \Rightarrow x=\dfrac{20000}{4.165} \\
 & \Rightarrow x=4801.92 \\
\end{align}\]
Hence, we got the value of x as x = Rs 4801.92.
Now the share of all sons combined was 33.34x.
Substituting the value of x, we get the share of sons as,
\[\begin{align}
  & 33.34(4801.92) \\
 & \Rightarrow 160096.013 \\
\end{align}\]
So, the share of one son can be obtained by dividing the above term by 3.
Therefore, the share of one son is,
\[\begin{align}
  & \dfrac{160096.013}{3} \\
 & \Rightarrow 53333.33 \\
\end{align}\]
Therefore, the share of one son is Rs 53333.33 i.e. option (a).

Note: The possibility of error in these types of questions can be at a point where you go for not assuming a variable but a random number, which would be wrong. Always go for assuming a variable other than some number.