Pipe A can fill an empty tank in 4 hours, and pipe B can empty the full tank in 6 hours. The tank is empty. The pipes are opened one at a time, for 1 hour each, in the order A, B, A, B, and so on, starting with A. After how many hours will the tank be full for the first time?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 19 hours
Take the capacity as the LCM of 4 and 6, that is 12 units. Each 2-hour round (A then B) adds only 1 unit, but the tank becomes full during an hour of A, before B can let water out, so look for the round after which one hour of A is enough.
A fills \(\frac{12}{4}=3\) units and B empties \(\frac{12}{6}=2\) units per hour
Net gain in one round (A then B) \(=3-2=1\) unit
The tank fills in an hour of A once the level at the start of that hour is \(12-3=9\) units
9 units are reached after 9 rounds \(=9\times2=18\) hours
19th hour (A): \(9+3=12\) units, full
One round earlier the level was 8 units, and A takes it only to 11 units, so the tank is not full before 19 hours