Question : Three pipes A, B, and C can fill a cistern in 6 hours. After working at it together for 2 hours, C is closed and, A and B fill it in 7 hours more. The time taken by C alone to fill the cistern is:
Option 1: 14 hours
Option 2: 15 hours
Option 3: 16 hours
Option 4: 17 hours
Correct Answer: 14 hours
Solution :
In 1 hour (A + B + C) fills $\frac{1}{6}$ part of the tank.
In 2 hours (A + B + C) fills $\frac{1}{6}$ × 2 = $\frac{1}{3}$ part of the tank.
In 7 hours (A + B) fills the remaining $(1-\frac{1}{3}$) = $\frac{2}{3}$ part of the tank.
In 1 hour (A + B) fills $\frac{2}{21}$ of the tank.
Therefore, C's 1 hour of work = (A + B + C)'s 1-hour work – (A + B)'s 1-hour work $=\frac{1}{6}-\frac{2}{21}=\frac{1}{14}$
So, C alone can fill the tank in 14 hours.
Hence, the correct answer is 14 hours.
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