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Question

If $$4$$ men and $$6$$ women can do a piece of work in $$24$$ days, then how many men should join $$3$$ women to complete the work in $$16$$ days?


A
2
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B
4
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C
5
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D
6
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Solution

The correct option is A $$4$$
The work requires $$4 \times 24$$ = 96 man-days or $$6 \times 24$$ $$= 144$$ woman-days.
In other words $$1$$ man is equivalent of $$1.5$$ women.
If $$3$$ women are available for $$16$$ days they would do $$3\times16 = 48 $$woman-days of work. The balance of $$144–48 = 96$$ woman-days has to be done by the men.
$$96$$ woman-days $$= 64$$ man-days. 
Now these $$64$$ man-days of work is to be completed in $$16$$ days or $$4$$ men are adequate.
So $$3$$ women and $$4$$ men can completed the work in 16 days.

Maths

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