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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 the workers are without children??

a)5/18       b) 4/9     c)11/18     d)17/36

my answer is 11/18 but given to be correct is 5/18??help guys.. but please mention the complete procedure.

1 Answer

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Workers without children = men without children + women without children

Let $X$ be the total workers.

Women with children = X/3 * 1/2 * 1/3 = X/18

Men with children = 2X/3 * 3/4 * 2/3 = X/3

So, workers without children = X - X/18 - X/3 = 11/18

Now married workers without children = married women without children + married men without children

= X/3 * 1/2 * 2/3 + 2X/3 * 3/4 * 1/3 = X/9 + X/6 = 5/18

May be this is what is meant in question.
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