Question : 5 men can complete a work in 12 days, and 6 women can complete the same work in 20 days. In how many days can 1 man and 1 woman together complete this work?
Option 1: 120 days
Option 2: 32 days
Option 3: 40 days
Option 4: 60 days
Correct Answer: 40 days
Solution :
Given,
5 men can complete a work in 12 days, and 6 women can complete the same work in 20 days.
We know,
If A does $x$ amount of work in a day and B does $y$ amount of work in a day, then the total work done by both together, in a day = $\frac1x+\frac1y$
Work done by 1 man in a day $=\frac{1}{12×5}=\frac{1}{60}$
Work done by 1 woman in a day $=\frac{1}{6×20}=\frac{1}{120}$
Work done by 1 man and 1 woman in a day $=\frac{1}{60}+\frac{1}{120}=\frac{3}{120}=\frac{1}{40}$
So, the number of days in which 1 man and 1 woman together can complete the work is 40.
Hence, the correct answer is 40 days.
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