Question

In a certain office, $\dfrac{1}{3}$ of the workers are women, $\dfrac{1}{2}$ of the women are married and $\dfrac{1}{3}$ of the married women have children. If $\dfrac{3}{4}$ of the men are married and $\dfrac{2}{3}$ of the married men have children, what part of workers are without children.

Answer 1

Hint:
In this problem we suppose the total number of workers $x$ and then subtract total workers having children from $x$ and then find the number of children in the case of men and women both.

Complete step-by-step answer:
Given: Total women worker $ = \dfrac{1}{3}$ of workers
Total married women are $\dfrac{1}{2}$ and $\dfrac{1}{3}$ of the married women have children.
Total married men $\dfrac{3}{4}$ and $\dfrac{2}{3}$ of married men have children.
Let the total number of workers be x.
Then number of women is $\dfrac{x}{3}$
Number of men is $x - \dfrac{x}{3} = \dfrac{{2x}}{3}$
Now calculate number of women having children equal to
$\dfrac{1}{3}$ of married women $\dfrac{1}{2}$ of total women and $\dfrac{1}{3}$ of total workers.
It gives,
 $ = \dfrac{1}{3} \times \dfrac{1}{2} \times \dfrac{x}{3}$
$ = \dfrac{x}{{18}}$
So, the number of women having children is $\dfrac{x}{{18}}$ .
Now, calculate number of men having children
It is equal to $\dfrac{2}{3}$ of married men and $\dfrac{3}{4}$ of men and $\dfrac{2}{3}$ of total worker
It gives
$
   = \dfrac{2}{3} \times \dfrac{3}{4} \times \dfrac{{2x}}{3} \\
   = \dfrac{x}{3} \\
 $
So, number of men having children is $\dfrac{x}{3}$
Number of worker having children is
Men’s worker having children $ + $ women worker having children
$\dfrac{x}{{18}} + \dfrac{x}{3}$
Find the sum, $\dfrac{{7x}}{{18}}$ .
Therefore, workers having no children is
Total workers $ - $ worker having children
That is, $x - \dfrac{{7x}}{{18}} = \dfrac{{11}}{{18}}x$
it means $\dfrac{{11}}{{18}}$ of all workers are the workers having no children.
Hence, the correct option is D.

Note:
In such types of problems, do not try to solve it theoretically, as we have to imagine the number of children, so here we can imagine $x$ number of children.