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Pipes and Cisterns Questions with Solutions

Pipes and Cisterns is Time and Work with one twist — an outlet pipe drains the tank instead of filling it, so its rate is negative. Here’s the concept, four fully worked examples, and a few to try yourself.

The concept, quickly

  • A pipe that FILLS a tank has a positive rate (fraction of the tank filled per hour); a pipe that EMPTIES it (an outlet) has a negative rate. Combine rates exactly like Time and Work, but outlet pipes subtract.
  • If a filling pipe can fill a tank in x hours, its rate is 1/x. If an outlet can empty a full tank in y hours, its rate is −1/y.
  • With multiple pipes open together, add up all the rates (filling positive, emptying negative) to get the net rate. Time to fill (or empty) = 1 ÷ |net rate|, and the sign tells you which direction the tank is actually moving.
  • A pipe that’s "twice as fast" as another has half the time — rate and time are inverses here just like in Time and Work.

Worked examples

1. Pipe A can fill a tank in 6 hours, and Pipe B can fill the same tank in 8 hours. If both pipes are opened together, how long will it take to fill the tank?

Solution

  1. Rate A = 1/6, Rate B = 1/8. Combined rate = 1/6 + 1/8 = 4/24 + 3/24 = 7/24.
  2. Time = 1 ÷ (7/24) = 24/7 = 3 3/7 hours.

Answer: 24/7 hours = 3 3/7 hours

2. Pipe A can fill a tank in 5 hours, while Pipe B (an outlet) can empty the full tank in 10 hours. If both pipes are opened together, how long will it take to fill the empty tank?

Solution

  1. Rate A = 1/5, Rate B = −1/10. Combined rate = 1/5 − 1/10 = 2/10 − 1/10 = 1/10.
  2. Time = 1 ÷ (1/10) = 10 hours.

Answer: 10 hours

3. Two pipes can fill a tank in 12 hours and 15 hours respectively. A third outlet pipe can empty the full tank in 20 hours. If all three are opened together, how long will it take to fill the empty tank?

Solution

  1. Rates: 1/12, 1/15, and −1/20. Using 60 as a common denominator: 5/60 + 4/60 − 3/60 = 6/60 = 1/10.
  2. Time = 1 ÷ (1/10) = 10 hours.

Answer: 10 hours

4. A tank can be filled by Pipe A in 4 hours. Pipe A is twice as fast as Pipe B. If both pipes work together, how long will they take to fill the tank?

Solution

  1. Pipe A’s rate = 1/4. "A is twice as fast as B" means A’s rate is double B’s rate, so B’s rate = (1/4) ÷ 2 = 1/8 (B alone would take 8 hours).
  2. Combined rate = 1/4 + 1/8 = 2/8 + 1/8 = 3/8.
  3. Time = 1 ÷ (3/8) = 8/3 = 2 2/3 hours.

Answer: 8/3 hours = 2 2/3 hours

Try these yourself

Work through these the same way, then check against the answer.

1. Pipe A can fill a tank in 10 hours, and Pipe B can fill the same tank in 15 hours. If both are opened together, how long will it take to fill the tank?

Answer: 6 hours

2. Pipe A can fill a tank in 6 hours, while Pipe B (an outlet) can empty the full tank in 9 hours. If both are opened together, how long will it take to fill the empty tank?

Answer: 18 hours

3. A tank can be filled by Pipe A in 12 hours. Pipe A is 3 times as fast as Pipe B. If both work together, how long will they take to fill the tank?

Answer: 9 hours

Where this comes up

Pipes and Cisterns is tested directly in the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — as a direct extension of Time and Work.

Practice more Pipes and Cisterns questions

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