Three men, four women and six children can complete a work in 9 days. A women does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 9 days?

Given (3 Men + 4 Women + 6 Children) -----> 9 days

But W = 2M and C = M/2

Now, convert Men and Children into Women by

$3\frac{W}{2} + 4W + 6\frac{W}{4}=> \frac{3}{2} + 4 + \frac{3}{2} = 7 \mathrm{Women}$ 

Therefore, 7 women alone can complete this work in 9 days.