Question : Work done by 8 men is completed in 10 days. The same work can be completed in 12 days when done by 10 women. How many days will they take to complete when 4 men and 4 women are employed to perform the same job?
Option 1: 12
Option 2: 6
Option 3: 10
Option 4: 8
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Correct Answer: 12
Solution :
8 men complete a work in 10 days.
The work rate of one man = $\frac{1}{8\times 10}= \frac{1}{80}$
10 women complete a work in 12 days.
The work rate of one woman = $\frac{1}{10\times 12}= \frac{1}{120}$
4 men's work rate + 4 women's work rate = $4\times\frac{1}{80} + 4\times\frac{1}{120} = \frac{5}{60}$
So, total days to complete the work = $\frac{60}{5}$ = 12 days
Hence, the correct answer is 12.
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