Question

In an office, $\frac{1}{3}$ of the workers are women, $\frac{1}{2}$ of the women are married and $\frac{1}{3}$ of the married women have children. If $\frac{3}{4}$ of the men are married and $\frac{2}{3}$ 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 C $\frac{11}{18}$

Let the total number of workers be $x$. Then,
Number of women = $\frac{x}{3}$ and number of men = $(x-\frac{x}{3})$ = $\frac{2x}{3}$
Number of women having children = $\frac{1}{3}of\frac{1}{2}of\frac{x}{3}=\frac{x}{18}$.
Number of men having children = $\frac{2}{3}of\frac{3}{4}of\frac{2x}{3}=\frac{x}{3}$.
Number of workers having children = $(\frac{x}{18}+\frac{x}{3})=\frac{7x}{18}$.
Therefore, workers having no children = $(x-\frac{7x}{18})=\frac{11x}{18}=\frac{11}{18}$ of all workers.
Hence, option (C) is the correct answer.