Question : Working together, A, B, and C can complete a task in 12 days. A and B can do the task in 55 days and 66 days, respectively, if they work alone. In how many days can C do the task if he works alone?
Option 1: 22
Option 2: 44
Option 3: 20
Option 4: 40
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Correct Answer: 20
Solution :
Let the total work = LCM of (12, 55, and 66) = 660 units
Task completed in 1 day by A = $\frac{660}{55}$ = 12 units
Task completed in 1 day by B = $\frac{660}{66}$ = 10 units
Task completed in 1 day by A, B, and C together = $\frac{660}{12}$ = 55 units
Task completed in 1 day by C = 55 – 12 – 10 = 33 units
So, time taken by C to do the work alone = $\frac{660}{33}$ = 20 days
Hence, the correct answer is 20.
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