$4$ men and $3$ women finish a job in $6$ days. And $5$ men and $7$ women can do the same job in $4$ days. How long will $1$ man and $1$ woman take to do the work?

From the given conditions, the total work is 24 man-days plus 18 woman-days, and also 20 man-days plus 28 woman-days. Equating them gives 4 man-days equals 10 woman-days, so 1 man equals 2.5 women. Substituting into the first equation means 24 times 2.5 women plus 18 women equals 78 women for the total job. 1 man and 1 woman equal 3.5 women, so dividing 78 by 3.5 gives 156 divided by 7, which is 22 and 2 over 7 days.

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