15 men and 18 women together finish a work in 6 days.One man alone finishes that work in 150 days. One woman will finish the same work in

15/M + 18/W = 1/6
1/M = 1/150
So from these two equations we have
1/10 + 18/W = 1/6 => 18/W = 1/6-1/10 => 18/W = 1/15 => 1/W = 1/270, So one woman can finish the work 270 days.