If 6 men and 8 women can do a piece of work in 10 days; and 13 men and 24 women can do the same work in 4 days, then what is the ratio of daily work done by a man to that of a woman?

Let m be the daily work of a man and w be the daily work of a woman. The first condition gives 60m + 80w = 1 and the second condition gives 52m + 96w = 1. Setting the equations equal to each other yields 60m + 80w = 52m + 96w, which simplifies to 8m = 16w, establishing the ratio of daily work done by a man to a woman as 2 : 1.

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