12 men and 5 women can complete a piece of work in 2 days, whereas 4 men and 3 women can complete the same piece of work in 5 days. In how many days can 8 men complete the piece of work?

Let m be the daily work of a man and w be the daily work of a woman. The given statements form the equations 2(12m + 5w) = 1 and 5(4m + 3w) = 1, which simplifies to 24m + 10w = 1 and 20m + 15w = 1. Equating the two left sides gives 24m + 10w = 20m + 15w, which means 4m = 5w, so w = 4/5 m. Substituting this into the second equation gives 20m + 15(4/5 m) = 1, simplifying to 32m = 1, meaning one man does 1/32 of the job daily. The daily work of 8 men is 8/32 = 1/4 of the job, so it takes them 4 days to complete the work.

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