Numerical aptitude · Time and motion
Pipes and cisterns, made easy
💡 The idea
It is time and work with water: a filling pipe adds part of the tank each hour, a leak takes some away.
🚰 Tap fills 1/4 an hour→💧 Leak empties 1/12→Net 1/4 − 1/12 = 1/6
🧭 The method: 3 steps
- Write each pipe’s part per hour (1 ÷ hours).
- Add the fillers, subtract the emptiers.
- Time = 1 ÷ (net part per hour).
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
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✏️ Worked examples
Example 1. A tap fills a tank in 4 h; a leak empties it in 12 h. With both, how long to fill?
- Tap: +1/4. Leak: −1/12.
- Each hour: 3/12 − 1/12 = 2/12 = 1/6
- Time = 6 hours
⚡ Shortcut: (4 × 12) ÷ (12 − 4) = 48 ÷ 8 = 6.
Example 2. Pipes fill in 10 h and 15 h. Together?
- 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6
- Time = 6 hours
⚡ Shortcut: (10 × 15) ÷ (10 + 15) = 150 ÷ 25 = 6.
⚠️ Where people go wrong
- A leak or emptying pipe is subtracted, never added.
- Two pipes together are faster than either one alone.
📌 Remember
- Fill + leak: (a × b) ÷ (b − a)
- Two fillers: (a × b) ÷ (a + b)