# 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?

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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?

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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.