1. Same as time and work
Inlet pipe = positive work, outlet/leak = negative work. Use the LCM method with tank capacity = LCM.
| Case | Result |
|---|---|
| Two inlets a, b | ab/(a + b) |
| Inlet a, outlet b (b > a) | ab/(b − a) |
| Fills in a, with leak in t | Leak alone empties in at/(t − a) |
| Three pipes | 1/(1/a + 1/b − 1/c) |
2. Solved examples
A fills in 20 min, B in 30 → together 600/50 = 12 min.
Fills in 6 h, with leak 8 h → leak empties in 6 × 8/2 = 24 h.
A 12 h, B 15 h fill; C 20 h empties → LCM 60: 5 + 4 − 3 = 6/h → 10 h.
A and B (10 h and 15 h) opened; A closed after 3 h → done 3 × 5/30 = 1/2 → B fills the rest in 7.5 h.
Leak empties a full tank in 6 h; inlet 4 L/min; with inlet on, it empties in 8 h → capacity = 240 × 6 × 8/2 = 5,760 L.
Solved examples by question type
Each type that comes in the ASO paper, worked step by step. Try it yourself first, then read the solution.
Basic level
Example 1. Pipe A fills a tank in 9 hours and pipe B in 21 hours. Both together fill it in:
(a) 7 3/10 hours (b) 6 3/10 hours (c) 12 hours (d) 15 hours
Answer: (b) 6 3/10 hours
Solution: Together per hour = 1/9 + 1/21 = 0.16. Time = 6 3/10 hours.
Example 2. Two pipes A and B can fill a tank in 20 hours and 30 hours respectively. If both are opened together, the tank will be filled in:
(a) 12 hours (b) 10 hours (c) 14 hours (d) 25 hours
Answer: (a) 12 hours
Solution: 1/20 + 1/30 = 1/12. Time = 12 hours.
Example 3. Two pipes A and B can fill a tank in 10 hours and 15 hours respectively. If both are opened together, the tank will be filled in:
(a) 5 hours (b) 12 1/2 hours (c) 8 hours (d) 6 hours
Answer: (d) 6 hours
Solution: 1/10 + 1/15 = 1/6. Time = 6 hours.
ASO exam level
Example 4. A pipe fills a tank in 2 hours. Because of a leak at the bottom, it takes 2 2/3 hours to fill. The leak alone can empty the full tank in:
(a) 2/3 hours (b) 1 3/5 hours (c) 8 hours (d) 10 hours
Answer: (c) 8 hours
Solution: 1/2 − 1/L = 1/2.67 → 1/L = 0.12 → L = 8 hours.
Example 5. Pipes A and B fill a tank in 18 and 9 hours, and pipe C empties it in 16 hours. If all three are opened together, the tank fills in:
(a) 4 4/11 hours (b) 9 3/5 hours (c) 10 3/5 hours (d) 6 hours
Answer: (b) 9 3/5 hours
Solution: Net per hour = 1/18 + 1/9 − 1/16 = 0.1. Time = 9 3/5 hours.
Example 6. One pipe fills a tank 4 times as fast as another. Together they fill it in 19 hours. The slower pipe alone fills it in:
(a) 23 3/4 hours (b) 95 hours (c) 38 hours (d) 100 hours
Answer: (b) 95 hours
Solution: Slower = x hours, faster = x/4. Together rate = 5/x = 1/19 → x = 95 hours.
Example 7. One pipe fills a tank 4 times as fast as another. Together they fill it in 6 hours. The slower pipe alone fills it in:
(a) 12 hours (b) 35 hours (c) 30 hours (d) 7 1/2 hours
Answer: (c) 30 hours
Solution: Slower = x hours, faster = x/4. Together rate = 5/x = 1/6 → x = 30 hours.
Example 8. A pump can fill a tank in 12 hours. Because of a leak, it takes 15 hours. If the tank is full, the leak alone will empty it in:
(a) 60 1/70368744177664 hours (b) 72 1/70368744177664 hours (c) 30 hours (d) 30 1/140737488355328 hours
Answer: (a) 60 1/70368744177664 hours
Solution: Leak rate = 1/12 − 1/15 = 1/60. Leak empties it in 60 hours.
Example 9. Pipe A fills a tank in 4 hours and pipe B empties it in 6 hours. If both are opened together, the empty tank fills in:
(a) 2 2/5 hours (b) 14 hours (c) 2 hours (d) 12 hours
Answer: (d) 12 hours
Solution: Net = 1/4 − 1/6 = 1/12. Time = 12 hours.
Example 10. Pipes A and B fill a tank in 12 min and 16 min. Both are opened together. After how many minutes should B be closed so that the tank is full in 8.86 minutes?
(a) 4.19 min (b) 6.86 min (c) 4.67 min (d) 6.19 min
Answer: (a) 4.19 min
Solution: A works all 8.86 min: 8.86/12. B must do the rest: 1 − 8.86/12 = 0.26 → B runs 4.19 min.
Example 11. Pipes A and B fill a tank in 30 min and 40 min. Both are opened together. After how many minutes should B be closed so that the tank is full in 18 minutes?
(a) 16 min (b) 18 min (c) 2 min (d) 17.14 min
Answer: (a) 16 min
Solution: A works all 18 min: 18/30. B must do the rest: 1 − 18/30 = 0.4 → B runs 16 min.
Advanced level
Example 12. Pipes A and B can fill a tank in 9 and 25 hours. Both are opened together and A is closed after 5 hours. B fills the rest in:
(a) 20 hours (b) 7 1/9 hours (c) 6 1/9 hours (d) 2 1/5 hours
Answer: (c) 6 1/9 hours
Solution: In 5 h both fill 5×(0.15) = 0.76. Rest 0.24 by B alone = 0.24 × 25 = 6 1/9 hours.
Example 13. Pipes A and B can fill a tank in 16 and 20 hours. Both are opened together and A is closed after 3 hours. B fills the rest in:
(a) 13 1/4 hours (b) 14 1/4 hours (c) 17 hours (d) 10 3/5 hours
Answer: (a) 13 1/4 hours
Solution: In 3 h both fill 3×(0.11) = 0.34. Rest 0.66 by B alone = 0.66 × 20 = 13 1/4 hours.
Example 14. A leak can empty a full tank in 12 hours. An inlet pipe fills water at 8 litres a minute. When the tank is full and the inlet is opened, the tank empties in 28 hours due to the leak. The capacity of the tank is:
(a) 5,760 litres (b) 13,440 litres (c) 10,560 litres (d) 10,080 litres
Answer: (d) 10,080 litres
Solution: Inlet per hour = 480 L = C/12 − C/28 → C = 480×12×28/(28 − 12) = 10,080 litres.
Example 15. Pipes A and B fill a tank in 12 and 15 hours, and pipe C empties it in 20 hours. If all three are opened together, the tank fills in:
(a) 12 hours (b) 5 hours (c) 6 2/3 hours (d) 10 hours
Answer: (d) 10 hours
Solution: Net rate = 1/12 + 1/15 − 1/20 = 1/10. Time = 10 hours.
Topic-wise practice for Pipes and cisterns (Quant): Filling and emptying, taps opened alternately, leaks. Useful for OPSC ASO, OSSC, OSSSC and other Odisha exams.
Question types covered
- Two pipes filling together
- Filling pipe with an emptying pipe or leak
- Fraction of the tank filled
- Pipes opened alternately
- Pipe closed after some time