Question

A man left one-third of his property to his son, one-fourth of the remaining to his daughter and remaining for his wife. if the wife’s share was Rs.45000, then how much money did the man leave

Answer 1

Hint: - For solving these types of questions we should assume the total assets/property is $'x'$, then make division it and evaluate the amount.

Complete step by Step solution:
Let us assume that total property = $x$
We are given share of his son $ = \dfrac{1}{3}$ of $x = \dfrac{x}{3}$
Now, remaining property
$ = x - \dfrac{x}{3}$
  $ = \dfrac{{3x - x}}{3} = \dfrac{{2x}}{3}$
Similarly, share of the daughter
 $ = \dfrac{1}{4}$ of the remaining property
  $ = \dfrac{1}{4} \times \dfrac{{2x}}{3} = \dfrac{x}{6}$
Given, share of wife = Rs. 45000
We know that,
Total property = share of son + share of daughter + share of the wife
$x = \dfrac{x}{3} + \dfrac{x}{6} + 45000$
Evaluate for $x$
$
   \Rightarrow x - \dfrac{x}{3} - \dfrac{x}{6} = 45000 \\
   \Rightarrow \dfrac{{6x - 2x - x}}{6} = 45000 \\
   \Rightarrow \dfrac{{3x}}{6} = 45000 \\
   \Rightarrow \dfrac{x}{2} = 45000 \\
   \Rightarrow x = 2 \times 45000 \\
   \Rightarrow x = Rs.90000 \\
 $

$\therefore $ The total money/property = Rs. 90000

Note: - Always remember while calculating the share of each family member always takes a share of remaining property and proceed with the next step