Question 15
If 3 men or 4 women can do a job in 43 days, the number of days the same job is done by 7 men and 5 women is
Solution
The whole job equals $$3 \times 43 = 129$$ man-days and also $$4 \times 43 = 172$$ woman-days, so one man does $$\frac{1}{129}$$ and one woman $$\frac{1}{172}$$ of the job each day. Working together, 7 men and 5 women do $$\frac{7}{129} + \frac{5}{172} = \frac{28 + 15}{516} = \frac{43}{516} = \frac{1}{12}$$ of the job per day. Hence the job takes 12 days.
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