Pipes and Cisterns Notes for SSC Exams

Pipes and Cisterns is a simple application of time and work. Instead of workers, we have pipes that fill a tank (inlet) and pipes that empty it (outlet). One question comes from this chapter in most SSC exams. These pipes and cisterns notes for SSC explain the formulas, the LCM method and the leak problems with solved examples.

Basic Idea

• An inlet pipe fills the tank, so its work is positive.
• An outlet pipe (or a leak) empties the tank, so its work is negative.
• If a pipe fills a tank in x hours, its one-hour work is 1/x.
• The net work in one hour is the sum of positive and negative works.
• Time to fill the tank = 1 / net work in one hour.

Important Formulas

The LCM Method

Take the capacity of the tank as the LCM of the times of all the pipes. Then each pipe fills or empties a fixed number of units per minute. Inlets are positive and outlets are negative. If A fills in 12 minutes, B fills in 15 minutes and C empties in 20 minutes, take the capacity as 60 units. A = +5, B = +4, C = -3, so the net rate is 6 units per minute and the tank is filled in 60 / 6 = 10 minutes.

Alternate Opening of Pipes

When two pipes are opened one after the other, find the work done in one full cycle (two minutes or two hours). Then divide the capacity by the work in one cycle to find the number of cycles, and multiply by the cycle time. Take care of the last cycle, because the tank may fill in the middle of it.

Solved Examples

Example 1: Pipe A can fill a tank in 10 hours and pipe B in 15 hours. How long will they take together?
Solution: Time = 10 x 15 / (10 + 15) = 150 / 25 = 6 hours.

Example 2: Pipe A fills a tank in 12 hours and an outlet C empties it in 18 hours. If both are opened, in how many hours is the tank filled?
Solution: Net work = 1/12 - 1/18 = (3 - 2)/36 = 1/36. Time = 36 hours.

Example 3: A tank is normally filled in 6 hours, but due to a leak it takes 8 hours. In how many hours will the leak empty the full tank?
Solution: Time = 6 x 8 / (8 - 6) = 24 hours.

Example 4: Pipes A and B fill a tank in 12 and 15 minutes. Pipe C empties it in 20 minutes. If all are open, when will the tank be full?
Solution: LCM = 60. A = 5, B = 4, C = -3. Net = 6 per minute. Time = 60 / 6 = 10 minutes.

Example 5: Pipes A and B fill a tank in 10 and 15 minutes. They are opened alternately, starting with A. When will it be full?
Solution: LCM = 30. A = 3, B = 2. In 2 minutes the work is 5 units. Time = 30 / 5 x 2 = 12 minutes.

Example 6: A tank of 1,200 litres has an inlet filling at 20 litres per minute and an outlet emptying at 12 litres per minute. How long will it take to fill when both are open?
Solution: Net rate = 8 litres per minute. Time = 1200 / 8 = 150 minutes.

Quick Tips to Solve Faster

• Always use the LCM method with positive and negative units.
• For a leak, find the time taken by the leak alone using xy / (y - x).
• In the alternate opening, calculate the work done in one cycle first.
• If the tank is already part full or part empty, adjust the capacity accordingly.
• Check that the net rate is positive; if it is negative or zero, the tank will not fill.

Common Mistakes to Avoid

• Adding the time of an outlet pipe instead of subtracting its work.
• Using xy / (x + y) for an inlet and an outlet pipe.
• Ignoring the units of the capacity and the rate.
• Not checking the last partial cycle in alternate opening questions.
• Forgetting that the leak also works when the inlet pipe is open.

Quick Revision Points

• Inlet is positive and outlet is negative.
• Two inlets together: xy / (x + y).
• Inlet and outlet: xy / (y - x).
• Leak time = xy / (y - x), where x is the time without the leak and y is the time with it.
• Capacity = LCM of the times.

Practice Questions With Answers

1. Pipes A and B fill a tank in 20 and 30 minutes. How long will they take together?
   Answer: 12 minutes (20 x 30 / 50).
2. A pipe fills a tank in 8 hours and an outlet empties it in 12 hours. How long will it take to fill with both open?
   Answer: 24 hours (8 x 12 / 4).
3. A tank fills in 4 hours but takes 5 hours with a leak. In how many hours will the leak empty the tank?
   Answer: 20 hours (4 x 5 / 1).
4. Pipes A and B fill a tank in 6 and 12 minutes and C empties it in 12 minutes. How long will it take with all open?
   Answer: 6 minutes (LCM 12: 2 + 1 - 1 = 2).
5. A tank of 900 litres has an inlet of 30 litres per minute and an outlet of 20 litres per minute. How long will it take to fill?
   Answer: 90 minutes (900 / 10).
6. Pipes A and B fill a tank in 15 and 10 minutes. How long will they take together?
   Answer: 6 minutes (15 x 10 / 25).
7. Pipe A is twice as fast as pipe B, and together they fill a tank in 12 minutes. How long will A take alone?
   Answer: 18 minutes (A = 2, B = 1, total = 36).
8. Pipes A (12 minutes) and B (6 minutes) are opened alternately starting with A. When is the tank full?
   Answer: 8 minutes (LCM 12: A = 1, B = 2; 3 per 2 minutes).
9. An outlet empties a full tank in 9 hours. An inlet fills it in 6 hours. If both are open, how long will it take to fill?
   Answer: 18 hours (1/6 - 1/9 = 1/18).
10. Two inlets fill a tank in 10 and 15 minutes and an outlet empties it in 30 minutes. How long to fill with all open?
    Answer: 7.5 minutes (LCM 30: 3 + 2 - 1 = 4).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching SSC pipes and cisterns practice paper to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Time and Work Notes
• Speed, Distance and Time Notes
• Ratio and Proportion Notes
• Average Notes
• SSC Pipes and Cisterns Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What are pipes and cisterns?

These are problems in which pipes fill or empty a tank (cistern), and we find the time taken under different conditions.

How many questions come from pipes and cisterns in SSC exams?

Usually one question comes from this chapter in SSC CGL and CHSL Tier 1.

How is it related to time and work?

Inlet pipes work like workers and outlet pipes or leaks work like negative workers, so the same formulas apply.

What is the formula for an inlet and an outlet?

If an inlet fills in x hours and an outlet empties in y hours, the net time to fill is xy / (y - x) hours.

How do I solve leak problems?

If the tank fills in x hours normally and y hours with the leak, the leak alone empties it in xy / (y - x) hours.

What is the LCM method?

Take the capacity as the LCM of the times and find the units filled or emptied per hour by each pipe.

What if the net rate is negative?

Then the outlet is faster than the inlet and the tank will empty instead of filling.

How should I practise this chapter?

Learn the formulas, solve the examples here and then attempt the pipes and cisterns practice paper.