Question

In an office, ¼ of the employees are women. ⅔ of the women and ¾ of the men are married. If ¾ of the married women and 8/9 of the married men have children, then the fraction of the employees having no children among the total number of employees is
(1) ⅜
(2) ⅛
(3) ½
(4) ⅙

Answer 1

The answer must be 3/8.

Reasons: 1/4 are women then 3/4 are men.

2/3*[1/4]= 2/12 women are married while 3/4*[3/4] = 9/16 men are married.

3/4*[2/12]=1/8 women have children while 8/9[9/16]=4/8 men have children.

Thus total no. of people having children = 1/8+ 4/8= 5/8

Therefore total no. of people not having children= 1- 5/8= [8-5]/8= 3/8

Answer is (1) 3/8

hope that helps!