6 men and 5 women can do a work in 10 days. 4 men and 7 women can do a same work in 12 days. How long will 6 women and 12 men can take to do the work?

Let the one day work of a man be m and a woman be w. From the given information, 6m + 5w = 1/10 and 4m + 7w = 1/12. Multiplying the first equation by 2 and the second by 3 gives 12m + 10w = 1/5 and 12m + 21w = 1/4. Subtracting the first from the second gives 11w = 1/20, so w = 1/220. Substituting this back gives 4m + 7/220 = 1/12, which simplifies to 4m = 1/15, so m = 1/60. The combined one day work of 12 men and 6 women is 12/60 + 6/220 = 1/5 + 3/110 = 22/110 + 3/110 = 25/110 = 5/22. They will complete the work in 22/5 days, which is 5 1/2 days.

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