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

Since, 3 women + 18 children complete work in 2 days. Therefore, (3 x 2) women + (18 x 2) children complete work in 1 days i.e, 6 women + 36 children complete work in 1 day.
Work of 36 children for 1 day = 1 - (1/3) = 2/3
[∵ work of 6 women for 1 day = 1/3]
∴ 36 children do 2/3 part of the work in 1 day.
36 children can do the work in 3/2 days.
9 children can do the the work in (3/2) x 4 = 6 days