Three pipes A, B and C, opened together on an empty tank, can fill it in 6 hours. The tank is empty and all three are opened together. After 2 hours pipe C is closed, and pipes A and B fill the rest of the tank in another 7 hours. How long would pipe C alone take to fill the empty tank?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 14 hours
The first 2 hours give the part filled by all three; the next 7 hours give the rate of A and B together. C's rate is the joint rate of all three minus that of A and B.
A, B and C fill \(\frac{1}{6}\) per hour; in 2 hours \(\displaystyle =\frac{2}{6}=\frac{1}{3}\)
Part left \(\displaystyle =1-\frac{1}{3}=\frac{2}{3}\), filled by A and B in 7 hours
A and B together \(\displaystyle =\frac{2}{3}\div7=\frac{2}{21}\) per hour
C alone \(\displaystyle =\frac{1}{6}-\frac{2}{21}=\frac{7-4}{42}=\frac{1}{14}\) per hour
Pipe C alone fills the tank in 14 hours.