Discussion
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is
Answer: C
C alone takes 14 hours.
Working together, A, B and C fill 1/6 of the tank an hour, so in 2 hours they fill 1/3, leaving 2/3 for A and B:
\[ \begin{aligned} A + B &= \frac{2/3}{7} = \frac{2}{21} \text{ per hour} \\ C &= \frac{1}{6} - \frac{2}{21} = \frac{7 - 4}{42} \\ &= \frac{3}{42} = \frac{1}{14} \text{ per hour} \end{aligned} \]
So C alone fills the tank in 14 hours. Check: A and B alone would take 21/2 = 10.5 hours, and 1/10.5 + 1/14 = 1/6, the combined rate given. 10, 12 and 16 do not satisfy this.
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