How to Solve Pipes and Cisterns Problems
Solve pipes and cisterns aptitude problems with signed inlet/outlet rates — formulas, a worked example, and practice questions with answers.
Expected Interview Answer
Pipes and cisterns problems extend time-and-work: an inlet pipe fills at a positive rate (1/a of the tank per hour), an outlet pipe drains at a negative rate (−1/b per hour), and combined rates add, with a negative net rate meaning the tank empties.
Treat "fills in a hours" as a rate of +1/a per hour and "empties in b hours" as −1/b per hour, exactly like time-and-work but with a sign. When multiple pipes operate together, sum all the signed rates to get the net rate; time to fill or empty is 1 ÷ |net rate|, and the sign tells you whether the tank fills or drains. The LCM-as-total-capacity trick from time-and-work applies unchanged — assume tank capacity equals the LCM of all given times to avoid fractions.
- Directly reuses the time-and-work rate-addition method
- The only new idea is a sign for outlet pipes
- LCM trick still avoids fractional arithmetic
AI Mentor Explanation
A run chase where one batter scores at +8 runs per over (an "inlet") while a bowling spell effectively "removes" 3 runs per over of scoring opportunity through dot balls (an "outlet") gives a net rate of +5 runs per over. Pipes and cisterns work identically: an inlet pipe is a positive fill rate, an outlet pipe is a negative rate, and you sum the signed rates to get how fast the tank actually fills or drains.
Worked example (inlet and outlet together)
Inlet A
- Fills in 10 h → rate = +1/10 per h
Outlet B
- Empties in 15 h → rate = −1/15 per h
Net rate
- 1/10 − 1/15 = 1/30 per h
Time to fill
- 1 ÷ (1/30) = 30 hours
Step-by-Step Explanation
Step 1
Assign signed rates
Inlet pipes get +1/a per hour; outlet pipes get −1/b per hour.
Step 2
Sum all open pipes
Add every signed rate for pipes that are simultaneously open.
Step 3
Take the reciprocal magnitude
Time = 1 ÷ |net rate|.
Step 4
Read the sign
Positive net rate → tank fills; negative → tank empties.
What Interviewer Expects
- Correct sign convention for inlet vs outlet
- Rate addition reused from time-and-work
- Correct interpretation of a negative net rate
- Use of the LCM trick to avoid fractions
Common Mistakes
- Treating outlet pipes as positive rates
- Adding times instead of signed rates
- Not checking whether the net rate is negative (tank empties)
- Errors when a pipe opens or closes partway through
Best Answer (HR Friendly)
“It’s time-and-work with a sign. An inlet pipe filling in a hours is a rate of plus one-over-a per hour; an outlet pipe emptying in b hours is minus one-over-b per hour. Add up all the signed rates for the pipes running together, and the time to fill or drain is one divided by the size of that net rate — the sign tells you which direction it’s going.”
Follow-up Questions
- How do you handle a pipe that opens only after some hours have passed?
- What if the net rate comes out negative — what does that mean?
- How does this generalize to three or more pipes?
- How do pipes and cisterns problems relate to time-and-work problems?
MCQ Practice
1. Pipe A fills a tank in 6 hours. Pipe B (outlet) empties it in 12 hours. Both open together, time to fill?
Net rate = 1/6 − 1/12 = 2/12 − 1/12 = 1/12 of the tank per hour, so time to fill = 1 ÷ (1/12) = 12 hours.
2. An outlet pipe empties a full tank in 20 hours. Its rate is?
Outlet pipes drain the tank, so the rate is negative: −1/20 of the tank per hour.
3. Two inlet pipes fill a tank in 10 and 15 hours respectively. Together, how long do they take?
Net rate = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6, so time = 6 hours.
Flash Cards
Inlet pipe rate? — Positive: fills in a hours → +1/a per hour.
Outlet pipe rate? — Negative: empties in b hours → −1/b per hour.
Net rate rule? — Sum all signed rates of pipes open simultaneously.
Negative net rate means? — The tank is draining, not filling.