Two inlets and one outlet — Time & Work Aptitude Question
Two inlets and one outlet: Pipe A fills a tank in 6 hours, pipe B in 9 hours, and pipe C empties a full tank in 18… Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
Pipe A fills a tank in 6 hours, pipe B in 9 hours, and pipe C empties a full tank in 18 hours. With all three open, how long does the tank take to fill?
Options
- 4 h
- 4.5 h
- 5 h
- 6 h
Show the answer and the worked solution
Correct answer: B. 4.5 h
Worked solution
- Net rate = 1/6 + 1/9 − 1/18 = 3/18 + 2/18 − 1/18 = 4/18 = 2/9 of the tank per hour.
- Time = 9/2 = 4.5 hours.
Answer: 4.5 h.
The idea
Pipes are workers: inlets add rate, outlets subtract. Take the tank as 18 units (the LCM) and the rates become 3, 2 and −1 per hour, net 4, so 18/4 = 4.5.
Shortcut. Back-substitute: in 4.5 h A fills 3/4, B fills 1/2 and C drains 1/4 — net exactly one tank.
Common trap. 4 h — mistaking the net rate (3 + 2 − 1 = 4 units an hour on an 18-unit tank) for the time; the time is 18 ÷ 4 = 4.5 h.