Capacity from a waste pipe — Time & Work Aptitude Question
Capacity from a waste pipe: Two taps fill a cistern in 30 and 40 minutes. A waste pipe empties 3 gallons per minute. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 135 seconds
Question
Two taps fill a cistern in 30 and 40 minutes. A waste pipe empties 3 gallons per minute. With all three open the cistern fills in 60 minutes. What is the capacity of the cistern?
Options
- 60 gallons
- 72 gallons
- 84 gallons
- 96 gallons
Show the answer and the worked solution
Correct answer: B. 72 gallons
Worked solution
- 1/30 + 1/40 − w = 1/60. Over 120: 4/120 + 3/120 − w = 2/120.
- w = 5/120 = 1/24, so the waste pipe empties the cistern in 24 minutes.
- At 3 gallons per minute, capacity = 24 × 3 = 72 gallons.
Answer: 72 gallons.
The idea
Work in fractions of the cistern to find the waste pipe's emptying time, then convert to volume using its stated flow rate. The two units meet only at the last step.
Shortcut. Call the cistern 120 units: the taps give 7 a minute and the net is 2, so the waste pipe removes 5 units = 3 gallons a minute, and 120 units = 120 × 3/5 = 72 gallons.
Common trap. Multiplying the waste pipe's 3 gallons a minute by the 60-minute fill gives 180 gallons — what the pipe drains while the cistern fills, not what it holds; the pipe alone would empty the cistern in 24 minutes, so the capacity is 24 × 3 gallons.