A and B alone take 4 and 6 hours, respectively, to complete a certain work. If they work alternately each hour, starting with A first, how long will it take them to complete the work?
Show answer & explanation
Correct answer: A
Explanation
The Correct answer is option 1 i.e. hours
Given that
A can complete a certain work alone in 4 hours
B can complete that work alone in 6 hours
Total work = LCM (4, 6) = 12
The efficiency of A = 12/4 = 3
The efficiency of B = 12/6 = 2
If they work alternately each hour, starting with A first,
In 2 hours, (3 + 2 = 5) work will be completed
In 4 hours, 10 work will be completed
Remaining (12 - 10 = 2) work will be completed by A in 2/3 hours
Hence, total time take to complete this work is 4 + (2/3) = 14/3 hours