If 12 men and 16 women can do a piece of work in 5 days, while 13 men and 24 women can do the same in 4 days, then what will be the time taken by 15 men and 20 women to do the same work?

Calculate the total work in man-days by multiplying the workers by the days, giving 60 man-days plus 80 woman-days for the first group and 52 man-days plus 96 woman-days for the second group. Setting up the equations 60m plus 80w equals 52m plus 96w reveals that 8m equals 16w, meaning the capacity of 1 man is twice that of 1 woman. Converting the entire workforce to women, 15 men and 20 women equal 50 women, and since the total work from the first equation equals 200 woman-days, dividing 200 by 50 gives 4 days.

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