Question

A man leaves half his property to his wife, one third of his son and the remaining to his daughter. If the daughter’s share is Rs.$15,000$. How much money did the man leave? How much money did his wife get and what is his son’s share?
A) Now, the wife's share is $25,000$ Rs.
And the share of the son is $40,000$ Rs.
B) Now, the share of the wife is $65,000$ Rs.
And the share of the son $30,000$ Rs.
C) Now, the wife's share is $33,000$ Rs.
And share of the son $20,000$ Rs.
D) Now, the wife's share is $45,000$ Rs.
And the share of the son $30,000$ Rs.

Answer 1

Hint: When you read such kinds of problems where ratios are mentioned, assume the total to be $1$ part and divide the given ratios accordingly and calculate the solution. In case you get confused by this approach, you can also convert the ratios into percentages by taking the total as $100\% $.

Complete step-by-step answer:
Let the total property of the man to be assumed as x. Now this x consists of wife’s share, son’s share and the daughter’s share too. We need to calculate the individual share value as we are provided with the proportions in which the property is divided.
Then,
Given that, the wife's share is the half of the total property. Divide the entire property value with the two to get the value of the wife's share. This can be calculated by the following mathematical form:
Wife’s property share $ = \dfrac{1}{2} \times x$
Given that, the son's share is the one-third of the total property. Divide the entire property value with the three to get the value of the son's share. This can be calculated by the following mathematical form:

Son’s property share $ = \dfrac{1}{3} \times x$
Now, in order to find the daughter’s share we can deduct the shares of wife’s and son’s from the total share as the property is only being shared among those three people.

Daughter’s property $ = x - (\dfrac{1}{2} \times x) - (\dfrac{1}{3} \times x)$
                         $
   = x - x(\dfrac{1}{2} + \dfrac{1}{3}) \\
   = x - \dfrac{{5x}}{6} \\
   = \dfrac{x}{6} \\
 $
As per the data given the problem, we have a particular value. So, by equating the above derived equation with that value we can get the value of x
But in problem it is equal to the $15,000$ Rs.
So,
$
  \dfrac{x}{6} = 15,000 \\
  x = 6 \times 15,000 \\
  x = 90,000 \\
 $
Now, we obtained the value of total share. So, now we can calculate everyone’s share by using the above derived equations by substituting the value we obtained in those equations.
The value of the property that man has is $90,000$Rs.
Wife’s share $ = \dfrac{1}{2} \times x$
              $
   = \dfrac{1}{2} \times 90000 \\
   = 45,000 \\
 $
Son’s share $ = \dfrac{1}{3} \times x$
            $
   = \dfrac{1}{3} \times 90000 \\
   = 30000 \\
 $
So, the required shares of wife and son are $45,000$ Rs and $30,000$ Rs respectively.(Option D)

Note: This problem can be solved without using any variable also by assuming total to be $1$ part and rest all as ratios. Before solving such ratio problems firstly look at options so that you are able to eliminate some options according to the ratio given. For example, the wife's share is more than the son's share in this problem, so the options that are not following this can be eliminated.