Pipe A can fill an empty tank in 5 hours, and pipe B can empty the full tank in 7 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 2
The correct answer is Option (2) → 29 hours
Take the capacity as the LCM of 5 and 7, that is 35 units. Each 2-hour round (A then B) adds only 2 units, 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 \(\frac{35}{5}=7\) units and B empties \(\frac{35}{7}=5\) units per hour
Net gain in one round (A then B) \(=7-5=2\) units
The tank fills in an hour of A once the level at the start of that hour is \(35-7=28\) units
28 units are reached after 14 rounds \(=14\times2=28\) hours
29th hour (A): \(28+7=35\) units, full
One round earlier the level was 26 units, and A takes it only to 33 units, so the tank is not full before 29 hours