Pipes A and B can fill an empty tank in 4 hours and 6 hours respectively, and pipe C can empty the full tank in 3 hours. The tank is empty. The pipes are opened one at a time, for 1 hour each, in the order A, B, C, A, B, C, and so on, starting with A. After how many hours will the tank be full for the first time?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 23 hours
Take the capacity as the LCM of 4, 6 and 3, that is 12 units. Each 3-hour round adds only a little, but the tank can become full during an hour of A or B, before C lets water out, so the last rounds must be followed hour by hour.
A fills \(\frac{12}{4}=3\), B fills \(\frac{12}{6}=2\) units and C empties \(\frac{12}{3}=4\) units per hour
Net gain in one round (A, B, C) \(=3+2-4=1\) unit
After 6 rounds \(=18\) hours the tank holds 6 units; A and B take it to \(6+3+2=11\) units only, and C brings it down to 7
After 7 rounds \(=21\) hours the tank holds 7 units
22nd hour (A): \(7+3=10\); 23rd hour (B): \(10+2=12\) units, full
The tank is full for the first time after 23 hours.