How to Solve Pipes and Cisterns Problems with an Outlet
Solve pipes and cisterns problems with an outlet using signed rates, a worked example, and practice questions with full explanations.
Expected Interview Answer
Treat every inlet pipe as a positive rate and every outlet (leak) as a negative rate in “tank per hour” units, add all the signed rates together, then invert the combined rate to get the time to fill or empty the tank.
Convert each pipe's stated fill or empty time into a rate: a pipe that fills the tank in x hours contributes +1/x tank per hour, and one that empties it in y hours contributes -1/y. Sum the signed rates when all pipes are open together; if the net rate is positive the tank fills, if negative it drains, and the time taken is the reciprocal of the absolute net rate. When a problem asks how much longer filling takes because of a leak, compute the combined rate with the leak included and compare its reciprocal to the leak-free fill time. Always keep units consistent (same “tank” as 1 whole job) so the signed rates can be added directly.
- One signed-rate framework handles any mix of inlets and outlets
- Reciprocal of the net rate directly gives the combined time
- Avoids sign errors that come from treating leaks as separate cases
AI Mentor Explanation
A required run rate of 8 per over is like an inlet filling the target at +8 runs/over, while a string of dot balls and a wicket-forced slowdown act like a leak draining 2 runs/over off the required pace. The net scoring rate becomes 8 minus 2 equals 6 effective runs per over toward the target, and the overs needed is the target divided by that net rate, not the raw 8. Pipes and cisterns with an outlet work identically: add the inlet rate and subtract the outlet rate to get one net rate, then invert it for the time.
Worked example (inlet plus outlet)
Inlet A rate
- +1/6 tank/hr
Outlet B rate
- −1/12 tank/hr
Net time
- 1/6 − 1/12 = 1/12
- Fills in 12 hrs
Step-by-Step Explanation
Step 1
Convert times to rates
Fill time x hours → +1/x; empty time y hours → −1/y.
Step 2
Sum the signed rates
Add all open pipes' rates, inlets positive, outlets negative.
Step 3
Check the sign
Positive net rate fills the tank; negative net rate empties it.
Step 4
Invert for time
Time = 1 ÷ |net rate|, in the same time unit used for each pipe.
What Interviewer Expects
- Correctly signs inlets as positive and outlets as negative
- Adds rates before inverting, never inverts each pipe's time and adds those
- Interprets a negative net rate as the tank draining, not filling
- Keeps units consistent across all pipes in the problem
Common Mistakes
- Adding raw times instead of converting to rates first
- Forgetting to subtract the outlet's rate, treating it as another inlet
- Inverting the wrong sign and reporting an empty time as a fill time
- Mixing minutes and hours across different pipes without converting
Best Answer (HR Friendly)
“I convert every pipe into a rate of tank-per-hour, with inlets positive and outlets negative, add all of them together to get one net rate, and then take the reciprocal of that net rate to find the time. The sign of the net rate tells me immediately whether the tank is filling or draining overall.”
Follow-up Questions
- How do you handle a problem with two inlets and two outlets open together?
- What happens if the net rate comes out negative in a “how long to fill” question?
- How would you find how long the outlet alone takes if only the combined and inlet rates are given?
- How do you adapt this method if a pipe is opened partway through the process?
MCQ Practice
1. Pipe A fills a tank in 4 hours, Pipe B (leak) empties it in 8 hours. Both are opened together. Time to fill the tank?
Net rate = 1/4 − 1/8 = 1/8 tank/hr, so time = 8 hours.
2. A tank fills in 10 hours with a leak present, and would fill in 6 hours with no leak. The leak alone would empty a full tank in?
Leak rate = 1/6 − 1/10 = 1/15, so the leak alone empties the tank in 15 hours.
3. Two inlets fill a tank in 5 hours together; one outlet alone empties it in 20 hours. If all three are opened together, the tank fills in?
Net rate = 1/5 − 1/20 = 3/20, time = 20/3 ≈ 6.67 hours.
Flash Cards
How do you represent an outlet pipe's rate? — As a negative rate: −1/y for a pipe that empties the tank in y hours.
How do you find combined fill time with a leak? — Sum inlet and outlet signed rates, then take the reciprocal of the net rate.
What does a negative net rate mean? — The tank is draining overall rather than filling.
How do you isolate an unknown leak rate? — Leak rate = no-leak fill rate − with-leak fill rate.