in a certain office 1 3 of the workers are women 2of..., Simplification, General Mathematics

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 `3/4`of the married and `2/3` of the married men have children,what part of workers are without children ?

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

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+ AnswerC

+ ExplanationLet the total number of workers be x.

Then,`w =x/3`and `M = (2x)/3`

Women having children

`= 1/3 of 1/2 of 1/3 x = x/18`

Men having children

`= 2/3 of 3/4 of (2x)/3 = x/3`

Workers having children 

`= (x/18 + x/3) = (7x)/18`

Workers having no children 

`= (x - (7x)/18) = (11x)/18`

`= 11/18` of all workers.

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