The leak costs an hour — Time & Work Aptitude Question
The leak costs an hour: A pipe fills a cistern in 4 hours, but because of a leak it takes 1 hour longer. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A pipe fills a cistern in 4 hours, but because of a leak it takes 1 hour longer. How long would the leak alone take to empty a full cistern?
Options
- 10 h
- 15 h
- 20 h
- 24 h
Show the answer and the worked solution
Correct answer: C. 20 h
Worked solution
- Effective rate with the leak = 1/5 per hour.
- Leak rate = 1/4 − 1/5 = 5/20 − 4/20 = 1/20.
- The leak alone empties the cistern in 20 hours.
Answer: 20 h.
The idea
Filling rate minus observed rate gives the leak's rate. The extra hour is not the leak's time — that misreading gives 1 hour or 5.
Shortcut. Leak time = product ÷ difference of the two filling times: 4 × 5 ÷ (5 − 4) = 20 hours.
Common trap. 10 h — half of 4 × 5, from dividing by 2 as if the delay were two hours; the delay is one hour, so the product itself is the answer.