Question : Three pipes A, B, and C can fill a tank in 6 hours. After working together for 2 hours, C is closed and A and B fill the tank in 8 hours. The time (in hours) in which the tank can be filled by pipe C alone is:
Option 1: 10
Option 2: 12
Option 3: 8
Option 4: 9
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Correct Answer: 12
Solution :
Time taken by A, B, and C together to fill the tank = 6 hours
Part of the tank filled by A, B, and C together in an hour = $\frac{1}{6}$
Part of the tank filled by A, B, and C together in the first 2 hours = $\frac{2}{6}$
So, the remaining part of the tank filled by A and B together = 1 – $\frac{2}{6}$ = $\frac{4}{6}$
Time taken by A and B to fill the remaining part of the tank = 8 hours
Time taken by A and B to fill the full tank = 8 ÷ $\frac{4}{6}$ = $\frac{8 × 6}{4}$ = 12 hours
Part of the tank filled by A and B together in an hour = $\frac{1}{12}$
Part of the tank was filled by C alone in an hour
= (Part of the tank filled by A, B, and C together in an hour) – (Part of the tank filled by A and B together in an hour)
= $\frac{1}{6}$ – $\frac{1}{12}$
= $\frac{1}{12}$
So, the time taken by C alone to fill the tank = 12 hours
Hence, the correct answer is 12.
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