Question : A and B can do a certain work in 6 hours, and A, B, and C together take 4 hours to do the same. How long will it take for C alone to accomplish the task?
Option 1: 12 hours
Option 2: 4 hours
Option 3: 2 hours
Option 4: 6 hours
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Correct Answer: 12 hours
Solution :
1 hour task of (A + B) = $\frac{1}{6}$
1 hour task of (A + B + C) = $\frac{1}{4}$
The task done by C alone in a day
= $\frac{1}{4}-\frac{1}{6}$
= $\frac{6-4}{24}$
= $\frac{2}{24}$
= $\frac{1}{12}$
So C alone can complete the whole work in 12 hours.
Hence, the correct answer is 12 hours.
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