2 men or 3 women can do a piece of work in 16 days. In how many days c

1.	2 men or 3 women can do a piece of work in 16 days. In how many days can 4 men and 6 women do the same work?
Answer» Number of days required by 2 men to finish the work : 16 days Number of days required by 3 women to finish the work : 16 days Number of days required by 1 man to finish the work : 2 x 16 = 32 days Number of days required by 1 woman to finish the work : 3 x 16 = 48 days Work done by a man in one day: \(\frac{1}{32}\) Work done by a woman in one day: \(\frac{1}{48}\) Work done by 4 men in one day: \(4\times\frac{1}{32}=\frac{1}{8}\) Work done by 6 women in one day: \(6\times\frac{1}{48}=\frac{1}{8}\) Work done by 4 men and 6 women together in one day: \(\frac{1}{8}+\frac{1}{8}=\frac{2}{8}=\frac{1}{4}\) ∴ 4 men and 6 women together take 4 days to complete the work.

2 men or 3 women can do a piece of work in 16 days. In how many days can 4 men and 6 women do the same work?

Answer»

Number of days required by 2 men to finish the work : 16 days

Number of days required by 3 women to finish the work : 16 days

Number of days required by 1 man to finish the work : 2 x 16 = 32 days

Number of days required by 1 woman to finish the work : 3 x 16 = 48 days

Work done by a man in one day: \(\frac{1}{32}\)

Work done by a woman in one day: \(\frac{1}{48}\)

Work done by 4 men in one day: \(4\times\frac{1}{32}=\frac{1}{8}\)

Work done by 6 women in one day: \(6\times\frac{1}{48}=\frac{1}{8}\)

Work done by 4 men and 6 women together in one day: \(\frac{1}{8}+\frac{1}{8}=\frac{2}{8}=\frac{1}{4}\)

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