RRB Group D · Bite-size lessons
Pipes and Cisterns
About 7 min · Mathematics · English
Time worked out from the lesson's 526 words at 150 words a minute, plus a minute for each question.
Pipes and cisterns is a time-and-work variant in Railway Group D mathematics. Instead of workers completing jobs, you deal with pipes filling or emptying tanks. The core principle is identical: work done = rate × time. A pipe's rate is expressed as "tank per hour" (or minute), and questions test your ability to combine multiple pipes working together or alternately, handle leaks, and compute net filling or emptying time.
Key ideas
- Rate of work analogy: If a pipe fills a tank in n hours, its rate is 1/n tank per hour. If it empties in m hours, its rate is –1/m tank per hour.
- Net rate for combined pipes: Add individual rates algebraically. Inlet rates are positive, outlet (leak/drain) rates are negative. Net rate = (sum of inlet rates) – (sum of outlet rates).
- LCM method for assumed capacity: When pipes fill in a, b, c hours, assume tank capacity = LCM(a, b, c) litres. Then each pipe's efficiency is capacity/time in litres per hour. This avoids fractions in intermediate steps.
- Time to fill/empty together: If net rate is R tank/hour, time = 1/R hours. If net rate is negative, the tank empties; if positive, it fills.
- Partial work in cycles: When pipes operate alternately (e.g. A for 1 hour, B for 1 hour, repeat), calculate work done in one complete cycle, then see how many cycles are needed.
Watch out for
- Sign error on outlets: Forgetting to subtract the outlet rate or treating leak as positive. Fix: Always assign negative rate to any pipe that empties/leaks, then add algebraically.
- Unit mismatch: Mixing hours and minutes without conversion (e.g. one pipe in 90 minutes, another in 2 hours). Fix: Convert all times to the same unit before calculating rates.
- Inverting the final answer: Computing net rate correctly but forgetting time = 1/(net rate), writing the rate itself as the answer. Fix: Remember the rate is fraction of tank per hour; flip it to get hours to complete 1 tank.
Quick reference
- Single pipe rate: 1/T tank per hour if fills in T hours; –1/T if empties in T hours.
- Combined rate = sum of all inlet rates minus sum of all outlet rates.
- Time together = 1 / (combined rate). Flip the rate fraction.
- LCM trick: Assume capacity = LCM of all pipe times to avoid fraction arithmetic.
- Alternating pipes: Calculate one full cycle work, divide 1 by cycle work to find number of cycles, then handle the remainder.
Check yourself: 3 questions
1. A pipe can fill a tank in 12 hours. Due to a leak at the bottom, it takes 15 hours to fill the tank. How long will the leak alone take to empty the full tank?
2. Two pipes A and B can fill a tank in 20 hours and 30 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
3. A pipe can fill a tank in 8 hours. Another pipe can empty it in 12 hours. If both pipes are opened simultaneously, how long will it take to fill the empty tank?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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