If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 12 women together do the work?

40

Given that 12m = 20w => 3m = 5w

9 men + 12 women = 15 women + 12 women = 27 women
20 women can do the work in 54 days. So, 27 women can do it in (20 * 54) /27 = 40 days.