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?

Options

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

Answer

C

Explanation

Suppose total number of workers in the office = x
Number of woman workers ` = x/3`
` therefore` Number of man workers
` x = - x/3 = (3x - x)/(3) = (2x)/(3)`
Number of married woman workers ` = x/3 xx 1/2 = x/6`
Number of married woman workers who childern
` rArr x/6 xx 1/3 = (x)/(18)`
Number of married man workers ` = (2x)/(3) xx 3/4 = x/2`
Number of married man workers who have children
` = x/2 xx 2/3 = x/3`
Number of workers who have children ` = x/3 + (x)/(18)`
` = (6x + x )/(18) = (7x)/(18)`
Number of workers without children
` = x - (7x)/(18)= (18 x - 7 x)/(18) = 11/18 x`