Eight men and 24 women can finish a piece of work in one day while 12 men and 18 women can also finish it in one day. What is the time taken by 24 men and 72 women to finish the work?

Let m = work done by one man per day, w = by one woman. Then 8m + 24w = 1 and 12m + 18w = 1. Subtracting: 4m – 6w = 0, so m = 1.5w, or 2m = 3w. Substituting in 8m + 24w = 1: 8m + 16m = 1 (since 24w = 16m), so 24m = 1, m = 1/24. Now 24 men + 72 women = 24m + 72w = 24m + 48m = 72m = 72/24 = 3 units of work per day. Time = 1/3 of a day.