Ikkish Prep Logo
IKKISH PREP
Pipes and Cisterns Tricks for Bank SSC Exam
Back to Blog

🚿 Pipes & Cisterns: Complete Guide with LCM Shortcut Tricks

Master the LCM method — the fastest way to solve Pipes & Cistern problems. Covers filling pipes, emptying pipes (outlets), leaks, alternate opening, and combined work scenarios with 20+ solved examples.

Topic: Time & Work Reading Time: 20 mins Updated: August 2026 Basic to Advanced

Introduction to Pipes & Cisterns

Pipes and Cisterns is essentially a sub-topic of Time and Work, but with a twist — the "work" here is filling or emptying a tank. Every Bank (IBPS, SBI), SSC CGL/CHSL, and Railway NTPC exam includes 2–3 questions from this topic.

Understanding these key terms is essential:

If a pipe fills in A hours → Rate = 1/A per hour (positive)
If a pipe empties in B hours → Rate = –1/B per hour (negative)
Combined Rate = 1/A – 1/B | Time = 1 / (Combined Rate)

The LCM Shortcut Method (Fastest Approach)

The LCM Method eliminates fractions entirely and makes calculations much faster. Here's how:

  1. Assume the total capacity of tank = LCM of all given times.
  2. Calculate each pipe's work per hour (filling or emptying).
  3. Add up the net work per hour (fill = +, empty = –).
  4. Time = Total Capacity / Net Work per hour.
🧮 Example 1: Pipe A fills a tank in 12 hours and Pipe B fills it in 18 hours. How long will both take together?

LCM of 12 and 18 = 36 units (Total Capacity)
A's rate = 36/12 = 3 units/hour
B's rate = 36/18 = 2 units/hour
Combined rate = 3 + 2 = 5 units/hour
Time = 36/5 = 7.2 hours = 7 hours 12 minutes ✅
💡 Exam Trick: Always use LCM as the "total work" — it converts fractions into whole numbers, making the calculation 3x faster!

Type 1: Inlet + Outlet (Both Open)

When both an inlet and outlet pipe are open simultaneously, the net work = inlet rate – outlet rate.

🧮 Example 2: A pipe fills a tank in 10 hours. Another pipe empties it in 15 hours. If both are open, how long to fill the tank?

LCM of 10, 15 = 30 units
Filling rate = 30/10 = 3 units/hour
Emptying rate = 30/15 = 2 units/hour
Net rate = 3 – 2 = 1 unit/hour
Time = 30/1 = 30 hours ✅
🧮 Example 3: Pipes A, B fill in 20, 30 hours. Pipe C empties in 40 hours. All three open. Time to fill?

LCM of 20, 30, 40 = 120 units
A = 6/hr, B = 4/hr, C = –3/hr
Net = 6 + 4 – 3 = 7 units/hour
Time = 120/7 = 17 1/7 hours ✅

Type 2: Leak Problems

A leak is an outlet that opens without intention. If a pipe fills a tank normally in X hours but due to a leak it takes Y hours, find the leak time.

🧮 Example 4: A pipe fills a tank in 15 hours. Due to a leak, it takes 20 hours. In how many hours will the leak empty the full tank?

LCM of 15, 20 = 60 units
Filling rate = 60/15 = 4 units/hour
Net (with leak) = 60/20 = 3 units/hour
Leak rate = 4 – 3 = 1 unit/hour
Leak empties full tank in = 60/1 = 60 hours ✅
🧮 Example 5: Two pipes fill a tank in 8 and 12 hours. A drain empties it in 24 hours. With all open, when is the tank full?

LCM = 24 units
Pipe 1 = 3/hr, Pipe 2 = 2/hr, Drain = –1/hr
Net = 3 + 2 – 1 = 4 units/hour
Time = 24/4 = 6 hours ✅

Type 3: Alternate Opening Problems

Pipes open alternately (one hour each). This requires a cycle-based approach.

🧮 Example 6: Pipe A fills in 10 hrs, Pipe B fills in 15 hrs. They open alternately starting with A. When is the tank full?

LCM = 30 units total
A fills 3 units/hr, B fills 2 units/hr
In 2 hours (1 cycle): 3 + 2 = 5 units filled
In 12 hours (6 cycles): 6 × 5 = 30 units
Wait — 30 units = full tank, so it fills in exactly 12 hours ✅
💡 Exam Trick for Alternate Problems: Find work done in one complete cycle (2 hours). Then: Number of complete cycles = Total Work / Work per cycle. Check if any partial cycle is needed.

Type 4: Find Time for One Pipe When Combined is Known

🧮 Example 7: Two pipes together fill a tank in 12 hours. One pipe alone takes 20 hours. Find the other pipe's time.

Let the other pipe fill in x hours
1/20 + 1/x = 1/12
1/x = 1/12 – 1/20 = (5–3)/60 = 2/60 = 1/30
x = 30 hours ✅
🧮 Example 8: A tank is filled in 5 hours by pipes A and B together. A alone takes 8 hours. How long does B take alone?

1/B = 1/5 – 1/8 = (8–5)/40 = 3/40
B = 40/3 = 13.33 hours ≈ 13 hrs 20 min ✅

🚨 Top Mistakes in Pipes & Cisterns

❌ Mistake 1: Treating outlets as positive (filling) instead of negative (emptying).
✅ Fix: Inlet = POSITIVE. Outlet/Drain/Leak = NEGATIVE. Always assign signs before computing.
❌ Mistake 2: Using fraction method and making arithmetic errors with LCM.
✅ Fix: Always use the LCM Method — it eliminates fractions and reduces errors significantly.
❌ Mistake 3: In alternate opening problems, assuming the tank is full at cycle count × cycle work without verifying.
✅ Fix: Always check the final partial hour separately to confirm whether the tank fills during that hour.

📋 Quick Revision: Pipes & Cisterns at a Glance

Type Approach
Both inlets openAdd rates → Time = LCM / Sum
Inlet + Outlet openNet rate = Inlet – Outlet
Leak problemLeak rate = Normal rate – Actual rate
Find one pipe's time1/x = 1/combined – 1/known
Alternate openingWork per cycle × cycles + partial check

Practice Questions: Pipes & Cisterns (With Answers)

  1. Pipe A fills in 8 hrs, Pipe B fills in 12 hrs. Both open, time to fill?
    Answer: LCM=24. A=3/hr, B=2/hr. Net=5/hr. Time=24/5=4.8 hours
  2. A pipe fills tank in 20 hrs. A leak can empty it in 30 hrs. How long to fill with leak?
    Answer: LCM=60. Fill rate=3, Leak=2. Net=1/hr. Time=60 hours
  3. Two pipes together fill tank in 6 hrs. One alone takes 10 hrs. Find the other pipe's time.
    Answer: 1/x=1/6–1/10=(5–3)/30=2/30=1/15. x=15 hours
  4. Pipe A fills in 12 hrs, B in 15 hrs, C empties in 6 hrs. All three open. When full?
    Answer: LCM=60. A=5, B=4, C=–10. Net=5+4–10=–1/hr. Tank empties, never fills!
  5. A tank has an inlet and outlet. Inlet fills in 10 hrs. With both open it takes 30 hrs. Find outlet time.
    Answer: 1/outlet=1/10–1/30=3/30–1/30=2/30=1/15. Outlet empties in 15 hours

Previous Year Questions: Pipes & Cisterns in Exams

🏦 SBI Clerk 2023: Pipe A fills a cistern in 16 hours and Pipe B fills it in 12 hours. Pipe C can empty it in 8 hours. If all three are opened simultaneously, in how many hours will the cistern be filled?
Solution: LCM=48. A=3, B=4, C=–6. Net=3+4–6=1/hr. Time=48/1=48 hours ✅
🚂 Railway NTPC 2022: A cistern can be filled by Pipe X in 14 hours and by Pipe Y in 21 hours. An outlet pipe Z can empty it in 42 hours. Starting from empty, how long to fill?
Solution: LCM=42. X=3, Y=2, Z=–1. Net=4/hr. Time=42/4=10.5 hours ✅
🏦 IBPS Clerk 2023: Tap A can fill a tank in 6 hours, Tap B in 9 hours. Both are opened at 9 AM. At what time will the tank be 3/4th full?
Solution: LCM=18. A=3/hr, B=2/hr. Net=5/hr. 3/4 of 18=13.5 units. Time=13.5/5=2.7 hrs≈2 hrs 42 min. Tank 3/4 full at 11:42 AM ✅

Advanced Pipes & Cisterns: Partial Filling & Multiple Scenarios

Scenario: Tank is Already Partially Filled

When the tank is already some fraction full when pipes open, adjust the total work accordingly.

Example: Pipe A fills in 10 hrs, Pipe B fills in 15 hrs. The tank is already 1/3 full. How long to fill completely?
Remaining work = 1 – 1/3 = 2/3 of tank
LCM = 30 units total. Remaining = 20 units.
Combined rate = 3+2 = 5 units/hr
Time = 20/5 = 4 hours ✅

Scenario: Pipe Opened/Closed After Some Time

A pipe is opened for some hours, then closed, while another continues.

Example: Pipes A (fills in 8 hrs) and B (fills in 12 hrs) are opened together. After 2 hours, A is closed. How much more time for B to fill the tank?
In 2 hours both open: (1/8+1/12)×2 = (3+2)/24×2 = 10/24 = 5/12 filled
Remaining = 1–5/12 = 7/12
B alone fills 7/12 in: (7/12)×12 = 7 more hours ✅

Key Rules for Pipes & Cisterns

← Previous: Age Problems Back to Blog →