4 men can do as much work in 7 days as 6 women in the same time. Find the number of days required to finish the work by 8 men and 9 women working together.

Number of days taken by 4 men to complete the work = 74 mens' 1 day's work = 171 man's 1 day's work = 1288 mens' 1 day's work = 828 = 27Number of days taken by 6 women to complete the work = 76 womens' 1 day's work = 171 woman's 1 day's work = 1429 women's 1 day's work = 942 =314Now, 8 mens' + 9 womens' 1 day's work = 27 + 314 = 4+314 = 12So, number of days taken by 8 men and 9 women together to complete the work = 2

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4 men can do work in 7 days
so 1 man does 1/(4*7) = 1/28 of the work each day
6 women can do work in 7 days
so 1 woman does 1/(6*7) = 1/42 of the work each day

8 men can do 8*(1/28) = 8/28 =2/7 of the work each day
9 women can do 9*(1/42) = 9/42 of the work each day

Together they do 2/7 + 9/42  = 12/42 + 9/42 = 21/42 = 1/2 of the work each day

They would thus take 1/(1/2) = 2 days to finish the work
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