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in Commercial Mathematics by (30.3k points)
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3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to do it? 

A. 6 days 

B. 5 days 

C. 4 days 

D. 3 days

1 Answer

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Best answer

Number of days required by 3 men to finish the work : 12 days 

Number of days required by 5 women to finish the work : 12 days 

Number of days required by 1 man to finish the work : 3 x 12 = 36 days 

Number of days required by 1 woman to finish the work : 5 x 12 = 60 days

Work done by a man in one day: \(\frac{1}{36}\)

Work done by a woman in one day: \(\frac{1}{60}\)

Work done by 6 men in one day: \(6\times\frac{1}{36}=\frac{1}{6}\)

Work done by 5 women in one day: \(5\times\frac{1}{60}=\frac{1}{12}\)

Work done by 6 men and 5 women together in one day: \(\frac{1}{6}+\frac{1}{12}=\frac{3}{12}=\frac{1}{4}\)

∴ 6 men and 5 women together take 4 days to complete the work.

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