Question

In a certain office, (1/3) of the workers are women, (1/2) of the women are married and (1/3) of the married women have children. If (3/4) of the men are married and (2/3) of the married men have children, what part of workers are without children ?

• A. $\frac{5}{18}$
• B. $\frac{4}{9}$
• C. $\frac{11}{18}$
• D. $\frac{17}{36}$

Answer 1

The correct option is A $\frac{5}{18}$

The answer is option $A$

Let's assume the total number of workers to be $x$ (a random multiple of 3 which easy to work with)

$\Rightarrow$ Number of women workers$=1/3\text{(number of workers)}=\frac{x}{3}$

Number of married women$=1/2\text{(Number of Women)}=\frac{x}{6}$

Number of women with children$=1/3\text{(Number of Married women)}=\frac{x}{18}$

Number of women without children $=\text{Number of Married women-Number of women with children}=\frac{x}{6}-\frac{x}{18}=\frac{x}{9}\to \left(I\right)$

Number of men workers$=2/3\text{(number of workers)}=\frac{2x}{3}$

Number of married men$=3/4\text{(Number of men)}=\frac{x}{2}$

Number of men with children$=2/3\text{(Number of married men)}=\frac{x}{3}$

Number of men without children $=\text{Number of Married Men-Number of Married men with children}=\frac{x}{2}-\frac{x}{3}=\frac{x}{6}\to \left(II\right)$

Number of people without children $=\left(I\right)+\left(II\right)=\frac{x}{9}+\frac{x}{6}=\frac{5x}{18}$

Part of the workers without children$=\frac{\frac{5x}{18}}{x}=\frac{5}{18}$