Question : A can do a piece of work in 6 days, working 8 hours a day, while B can do the same work in 4 days, working 10 hours a day. If the work has to be completed in 5 days, how many hours do they need to work together in a day?
Option 1: $4$
Option 2: $5\frac{4}{11}$
Option 3: $6\frac{4}{11}$
Option 4: $4\frac{4}{11}$
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Correct Answer: $4\frac{4}{11}$
Solution :
Part of the work A completes in an hour in a single day $\frac{1}{6}\times\frac{1}{8}=\frac{1}{48}$
Part of the work B completes in an hour in a single day $\frac{1}{4}\times\frac{1}{10}=\frac{1}{40}$
Let the number of hours needed to work together in a day be $y$.
According to the question,
$5y \times(\frac{1}{48}+\frac{1}{40})=1$
⇒ $y = \frac{40 \times48}{88 \times 5}$
⇒ $y = \frac{48}{11} =4\frac{4}{11}$ hours
Hence, the correct answer is $4\frac{4}{11}$ hours.
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