5 men and 15 women can complete a task in 10 days, while 15 men and 5 women can complete it in 20 days. In how many days will 40 women complete the task?
4 days
Let one man do m units and one woman w units of work per day.
Total work = 10(5m + 15w) = 20(15m + 5w), so 50m + 150w = 300m + 100w, giving 50w = 250m and w = 5m.
Total work = 10(5m + 15 × 5m) = 800m, which in terms of women is 800m = 160w.
40 women need 160w ÷ 40w = 4 days.
Hence, the answer is 4 days.
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