Question

In an office, $\frac{1}{3}$ of the employees 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, then the part of employees without children is:

• A. $\frac{3}{18}$
• B. $\frac{5}{18}$
• C. $\frac{7}{18}$
• D. $\frac{11}{18}$

Hint:

Assume total = 1 to simplify percentage/fraction problems.

Answer 1

The Correct Option is D

Concept: Assume total employees = 1.
Step 1: Women and men.
\[ {Women} = \frac{1}{3},\quad {Men} = \frac{2}{3} \]
Step 2: Women with children.
\[ {Married women} = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6} \] \[ {Women with children} = \frac{1}{3} \times \frac{1}{6} = \frac{1}{18} \]
Step 3: Men with children.
\[ {Married men} = \frac{3}{4} \times \frac{2}{3} = \frac{1}{2} \] \[ {Men with children} = \frac{2}{3} \times \frac{1}{2} = \frac{1}{3} \]
Step 4: Total with children.
\[ \frac{1}{18} + \frac{1}{3} = \frac{1}{18} + \frac{6}{18} = \frac{7}{18} \]
Step 5: Without children.
\[ 1 - \frac{7}{18} = \frac{11}{18} \]
Hence, the required fraction is $\frac{11{18}$.