Pipes and Cisterns
Pipes and Cisterns
Pipes and cisterns is time and work with a sign: an inlet pipe does positive work (fills), an outlet pipe or a leak does negative work (empties). Use the same LCM method with the tank capacity as the total, subtract the emptying rates, and every NTPC question falls out.
1. Rules
Tank capacity = LCM of the given times (in units) Inlet: + rate Outlet or leak: − rate
Net rate = sum of inlet rates − sum of outlet rates Time = capacity (or required part) ÷ net rate
| Situation | Result |
|---|---|
| Inlets fill in x and y hours | Together xy/(x + y) hours |
| Inlet fills in x hours, outlet empties in y hours (y > x) | Tank fills in xy/(y − x) hours |
| Tank fills in x hours, but with a leak in y hours | Leak alone empties the full tank in xy/(y − x) hours |
| Fill only a fraction f of the tank | Time = f × capacity ÷ net rate |
| Pipe closed after t hours | Work done in t hours first, then the rest at the new rate |
| Pipes opened alternately | Complete cycles first, then the leftover with the next pipe |
| Rates in litres per minute | Capacity = rate × time; a pipe that fills in t minutes has rate C/t |
✗ Inlet 9 h and outlet 12 h together fill the tank in 21 h | ✓ Rates subtract: 1/9 − 1/12 = 1/36, so 36 h
✗ With a leak the tank fills in 8 h instead of 6 h, so the leak empties it in 2 h | ✓ Leak rate = 1/6 − 1/8 = 1/24, so it empties a full tank in 24 h
हिंदी नोट: भरने वाले पाइप का काम धनात्मक और खाली करने वाले पाइप या रिसाव का काम ऋणात्मक लीजिए। टंकी की क्षमता को समयों का ल.स. मानकर हर पाइप की प्रति घंटा दर निकालिए।
Exam Pointer: Verified NTPC patterns: inlet and outlet together, including the time to fill a fraction of the tank (December 2020, three June 2025 Graduate CBT-1 shifts), leak in the bottom (two June 2025 Graduate CBT-1 shifts), a leak or pipe closed after some time (two June 2022 CBT-2 shifts) and tank capacity from pipe rates (June 2025 Graduate CBT-1, litres per hour).
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Inlets and outlets together, including part of the tank
[PYQ: NTPC Graduate CBT-1 23-Jun-2025 Shift-1 | NTPC CBT-1 29-Dec-2020 Shift-2 | NTPC Graduate CBT-1 21-Jun-2025 Shift-3]
EXAM LEVEL
Q. Pipe A can fill a tank in 10 hours and pipe B in 15 hours. How long will both take together?
Capacity = 30 units; A 3, B 2 per hour, together 5. Time = 30/5 = 6 hours.
Answer: 6 hours
EXAMATLAS LEVEL
Q. An inlet fills a tank in 9 hours and an outlet empties the full tank in 12 hours. Both are opened on an empty tank. How long will it take to fill two-thirds of the tank?
Capacity = 36 units; inlet +4, outlet −3, net +1 per hour. Two-thirds = 24 units, so 24 hours. (The whole tank would take 36 hours.)
Answer: 24 hours
Pattern 2: A leak in the bottom
[PYQ: NTPC Graduate CBT-1 19-Jun-2025 Shift-2 | NTPC Graduate CBT-1 16-Jun-2025 Shift-1]
EXAM LEVEL
Q. A pipe can fill a tank in 6 hours, but because of a leak it takes 8 hours. In how much time can the leak empty the full tank?
Capacity = 24 units; pipe 4 per hour, pipe with leak 3 per hour, so the leak removes 1 per hour and empties the tank in 24 hours. Formula: 6 × 8/(8 − 6) = 24.
Answer: 24 hours
EXAMATLAS LEVEL
Q. A tap can fill a tank in 12 hours, and a leak can empty the full tank in 20 hours. The tap is opened on an empty tank; after 6 hours the leak is noticed and plugged. How long does it take to fill the tank in all?
Capacity = 60 units; tap +5, leak −3, net +2 per hour. In 6 hours 12 units are filled. The remaining 48 units at 5 per hour take 9.6 hours. Total = 15.6 hours (15 h 36 min).
Answer: 15.6 hours
Pattern 3: A pipe closed after some time, or pipes opened alternately
[PYQ: NTPC CBT-2 15-Jun-2022 Shift-2 | NTPC CBT-2 17-Jun-2022 Shift-2]
EXAM LEVEL
Q. Pipes A and B can fill a tank in 20 and 30 minutes. Both are opened together, and B is closed after 6 minutes. How long does it take to fill the tank?
Capacity = 60 units; A 3, B 2 per minute. In 6 minutes both fill 30 units. A fills the remaining 30 in 10 minutes. Total = 16 minutes.
Answer: 16 minutes
EXAMATLAS LEVEL
Q. Pipes A and B can fill a tank in 12 and 18 hours. They are opened alternately for one hour each, starting with A. In how many hours will the tank be full?
Capacity = 36 units; A 3, B 2 per hour, so each 2-hour cycle fills 5. Seven cycles (14 hours) fill 35 units. The last unit is filled by A (its turn) in 1/3 hour. Total = 14 1/3 hours (14 h 20 min).
Answer: 14 1/3 hours
Pattern 4: Tank capacity from pipe rates
[PYQ: NTPC Graduate CBT-1 5-Jun-2025 Shift-3]
EXAM LEVEL
Q. Pipe A fills water at 40 litres per minute and pipe B at 60 litres per minute. Together they fill a tank in 30 minutes. Find the capacity.
Together 100 litres per minute for 30 minutes: 3,000 litres.
Answer: 3,000 litres
EXAMATLAS LEVEL
Q. Pipe A can fill a tank in 16 minutes. Pipe B empties water at 8 litres per minute. With both open, the empty tank fills in 24 minutes. Find the capacity.
Let the capacity be C litres. A's rate = C/16, net rate = C/24. So C/16 − 8 = C/24, giving C(1/16 − 1/24) = C/48 = 8 and C = 384 litres.
Answer: 384 litres
60-Second Revision
- Capacity = LCM of times; inlets add, outlets and leaks subtract.
- Inlet x, outlet y (y > x): fills in xy/(y − x).
- Leak time = xy/(y − x) where x is the normal time and y the time with the leak.
- Closed or alternate pipes: work done first, then the rest at the new rate.
- Litres questions: rate = capacity ÷ time; set up one equation in C.
Next Step: Time and Work and Pipes done. Practise these in the ExamAtlas RRB NTPC 2026 mock tests; the LCM method should make each question a 40-second job.