Pipes A and B can fill an empty tank in 10 hours and 20 hours respectively, and pipe C can empty the full tank. The tank is empty and all three pipes are opened together. After 6 hours pipe C is closed, and pipes A and B fill the rest of the tank in another 4 hours. In how many hours can pipe C alone empty the full tank?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 12 hours
Take the capacity as the LCM of 10 and 20, that is 20 units. Work backwards: the last 4 hours of A and B show how much was filled in the first 6 hours, and that gives C's rate.
A fills \(\frac{20}{10}=2\) units and B fills \(\frac{20}{20}=1\) unit per hour
Last 4 hours (A and B): \(4\times(2+1)=12\) units
First 6 hours (A, B and C): \(20-12=8\) units, that is \(\frac{8}{6}=\frac{4}{3}\) units per hour
C empties \(\displaystyle 3-\frac{4}{3}=\frac{5}{3}\) units per hour
Time for C to empty the full tank \(\displaystyle =20\div\frac{5}{3}=20\times\frac{3}{5}=12\) hours
Pipe C alone empties the full tank in 12 hours.