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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Question : Working 5 hours a day, A can complete a task in 8 days, and working 6 hours a day, B can finish the same task in 10 days. Working 8 hours daily, they can jointly complete the task in _____.
Option 1: 5 days
Option 2: 3 days
Option 3: 4.5 days
Option 4: 6 days
Question : 10 women can do a work in 6 days and 6 men can do the same work in 5 days. If all these men and women work together, then how many days will they take to finish this work?
Option 1: $2\frac{8}{11}$
Option 2: $4\frac{6}{11}$
Option 3: $1\frac{2}{11}$
Option 4: $3\frac{4}{11}$
Question : A can do a piece of work in 9 days, while B can do it in 12 days. A and B together can do the work in:
Option 1: $5\frac{1}{7}$ days
Option 2: $5\frac{2}{7}$ days
Option 3: $6\frac{1}{7}$ days
Option 4: $6\frac{2}{7}$ days
Question : Two workers A and B are engaged to do a piece of work. Working alone A would take 8 hours more to complete the work than when working together. If B worked alone, would take $4\frac{1}{2}$ hours more than when working together. The time required to finish the work together is:
Option 1: 5 hours
Option 2: 4 hours
Option 3: 8 hours
Option 4: 6 hours
Question : If 90 men can do a certain job in 16 days, working 12 hours per day, then the part of that work which can be completed by 70 men in 24 days, working 8 hours per day is:
Option 1: $\frac{1}{3}$
Option 2: $\frac{2}{3}$
Option 3: $\frac{7}{9}$
Option 4: $\frac{5}{8}$
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