Question : If a man completed a work in 10 days and the same work was completed by a woman in 8 days. How many days will it take to complete if they work together?
Option 1: $\frac{38}{8}$
Option 2: $\frac{40}{7}$
Option 3: $\frac{40}{9}$
Option 4: $\frac{42}{9}$
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Correct Answer: $\frac{40}{9}$
Solution :
According to the question,
One day work of a man = $\frac{1}{10}$th of the total work
One day work of a woman = $\frac{1}{8}$th of the total work
When they both work together 1 day work = $\frac{1}{10} + \frac{1}{8} = \frac{5+4}{40} = \frac{9}{40}$th of the total work
They both complete the work in $\frac{40}{9}$ days.
Hence, the correct answer is $\frac{40}{9}$.
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