From nine hours to ten — Time & Work Aptitude Question
From nine hours to ten: A cistern is normally filled in 9 hours, but a leak makes it take 10 hours. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
A cistern is normally filled in 9 hours, but a leak makes it take 10 hours. How long would the leak alone take to empty the full cistern?
Options
- 45 h
- 60 h
- 75 h
- 90 h
Show the answer and the worked solution
Correct answer: D. 90 h
Worked solution
- Leak rate = 1/9 − 1/10 = 10/90 − 9/90 = 1/90.
- The leak alone empties it in 90 hours.
Answer: 90 h.
The idea
A small delay implies a very slow leak. When two times are close, the difference of their reciprocals is tiny and the answer is large.
Shortcut. Leak time = product ÷ difference of the two filling times: 9 × 10 ÷ (10 − 9) = 90 hours.
Common trap. 45 h — half of 9 × 10, from dividing by 2 as if the delay were two hours; with a one-hour gap, product ÷ difference = 90 ÷ 1.