3 men or 5 women can do a work in 12 days. How long will 6 men and 5 w

1.	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
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.

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

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.