Question : It takes A and B, 3 and 6 hours, respectively, to complete a certain work. If they work on the alternate hour. How long will it take them to accomplish the task?
Option 1: 3 hours
Option 2: 4 hours
Option 3: 2 hours
Option 4: 4.5 hours
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Correct Answer: 4 hours
Solution :
A takes 3 hours to finish the work B takes 6 hours
A's 1-hour work = $\frac{1}{3} $
B's 1-hour work = $\frac{1}{6}$
Work completed in two hours with A and B working for one hour each alternatively = $\frac{1}3+\frac{1}6
= \frac{1}2$
So, number of 2 hours required to complete the work = $\frac{1}{\frac{1}{2}}$ = 2
Hence, the number of hours required to complete the work = 2 × 2 = 4 hours
Hence, the correct answer is 4 hours.
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