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Time and Work

In a certain ...

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

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Solution

Total women=1/3
in which married =1/2 of 1/3
=1/6
Women who has child=1/3 of married women
=1/3 of 1/6= 1/18
Total men =2/3 (as 1/3 are women)
Married man=3/4 of total man
=3/4 of 2/3=1/2
Man who has child=2/3 of married man
=2/3 of 1/2 =1/3
child having man+women=1/18+1/3=7/18
part that don't have child=1-7/18
=11/18

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