Question

Choose the most appropriate option.
In an office, $1/3$ of the workers are Men, $1/2$ of the men are married and $1/3$ of the married men have children. If $3/4$ of the women are married and $2/3$ of the married women have children, then the part of workers without children are:

• A. $11/18$
• B. $17/36$
• C. $5/18$
• D. $4/9$.

Answer 1

Answer: (A)

$11/18$

Let the total number worker be $x.$

$\Rightarrow$ Number of men in office $=\frac{1}{3}\times x=\frac{x}{3}$

$\Rightarrow$ Number of married men in office $=\frac{1}{2}\times \frac{x}{3}=\frac{x}{6}$

$\Rightarrow$ Number of married men having children $=\frac{1}{3}\times \frac{x}{6}=\frac{x}{18}$

$\Rightarrow$ Number of women in office $=x-\frac{x}{3}=\frac{2x}{3}$

$\Rightarrow$ Number of married women in office $=\frac{3}{4}\times \frac{2x}{3}=\frac{x}{2}$

$\Rightarrow$ Number of married women having children $=\frac{2}{3}\times \frac{x}{2}=\frac{x}{3}$

$\Rightarrow$ Total worker with children $=\frac{x}{18}+\frac{x}{3}$

$=\frac{7x}{18}$

$\Rightarrow$ Total worker without children $=x-\frac{7x}{18}$

$=\frac{11x}{18}$

$\therefore$ Number of worker without children is $\frac{11}{18}$ of total worker.