3 men and 18 women together take 2 days to complete a piece of work. How many days will 9 women alone take to complete the piece of work; if 6 men alone can complete the piece of work in 3 days?

Let the work done by 1 man and 1 woman in 1 day, m and w, respectively.

It is given that 3 men and 18 women together take 2 days to complete a piece of work.

Total work = (3m+18w)*2

6 men alone can complete the piece of work in 3 days = 6m*3 = 18m

Work done is the same for both cases.

So, 18m = 6m+36w

12m = 36w

m = 3w

Total work = 18m = 18*3w = 54w

Therefore, 9 women will complete the work in x days. = 9w*x = 54w

Thus, x = 6 days.