Capacity from a tap and a leak — Aptitude Question
Capacity from a tap and a leak: A leak can empty a full tank in 8 hours. With a tap admitting 6 litres per minute… Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 150 seconds
Question
A leak can empty a full tank in 8 hours. With a tap admitting 6 litres per minute also open, the full tank empties in 12 hours. What is the capacity of the tank?
Options
- 4,320 L
- 5,760 L
- 8,640 L
- 10,080 L
Show the answer and the worked solution
Correct answer: C. 8,640 L
Worked solution
- Leak rate = 1/8; net emptying rate with the tap = 1/12.
- Tap rate = 1/8 − 1/12 = 3/24 − 2/24 = 1/24, so the tap fills the tank in 24 hours.
- The tap delivers 6 × 60 = 360 litres per hour.
- Capacity = 24 × 360 = 8,640 litres.
Answer: 8,640 L.
The idea
Find the tap's filling time from the two emptying rates, then multiply by its flow. Converting litres per minute to litres per hour is where units usually go astray.
Shortcut. The tap's filling time is product ÷ difference of the two emptying times: 8 × 12 ÷ 4 = 24 hours, and 24 × 360 L = 8,640 L.
Common trap. 4,320 L — multiplying the tap's 360 L an hour by the 12-hour emptying time instead of the tap's own 24-hour filling time.