Pipes and Cisterns: Formula Sheet, Shortcuts and 12 Solved Questions

A tank, two pipes filling it, one pipe draining it, all open at once. The question asks how long until the tank is full, and your pen hovers because the time and work formula you trust does not have a slot for a pipe that works against you. That single image is where most aspirants lose the topic. Pipes and cisterns CAT 2026 questions are time and work in disguise, with one extra rule: some agents add work and some remove it. Miss the sign on the drainer and your whole calculation tilts the wrong way. Get the sign convention right and this entire topic becomes a one-line division.

Here is the honest part. Aspirants study pipes and cisterns as a separate chapter, memorise a fresh set of formulas, and then freeze the moment two fillers and a drainer share a tank. The fix is not more formulas. It is seeing that a filler is a plus rate, a drainer is a minus rate, and the net rate runs the show.

Why pipes and cisterns is just time and work

Strip the labels and the two topics are the same machine. In time and work, a person finishes a job in some number of days, so their rate is one job per that many days. In pipes and cisterns, a pipe fills a tank in some number of hours, so its rate is one tank per that many hours. The tank is the job. The pipe is the worker. Nothing new so far.

The one genuine difference is the emptying pipe. A worker never un-builds a wall, but a drain pipe absolutely removes water that fillers have added. So pipes and cisterns has negative work, which standard time and work problems do not. This is the same family of rate logic you saw in our guide to time and work DILR sets, only now one of the rates points downward. Once you accept the minus sign, every method you already own transfers cleanly.

It also rhymes with another topic aspirants overcomplicate. In our breakdown of boats and streams, the stream adds speed downstream and subtracts it upstream. Same plus and minus, different costume. CAT keeps recycling one idea, signed rates that combine into a net, across topic after topic. Spot the pattern and you stop studying three chapters when you really have one.

The 6-formula sheet

Six relationships cover almost every pipes and cisterns question CAT can ask. Learn them as rates, not as plug-in templates, and they stay flexible when the question gets strange.

Formula 4 carries a quiet warning. If the drainer is faster than the filler, the net rate is negative and the tank never fills, it empties. Always check which way the net points before you reach for the time. That single check separates a confident answer from a sign error.

The net-work sign convention

This is the heart of the topic, so slow down here. Every pipe gets a sign before it gets a number. A filler is plus. A drainer is minus. You write each pipe as a signed rate, add them all into one net rate, and then the tank behaves like a single pipe running at that net speed.

Walk through it once. Three pipes share a tank: pipe one fills in 6 hours, pipe two fills in 8 hours, pipe three drains in 12 hours. Signed rates are plus 1/6, plus 1/8, minus 1/12. Take the LCM of 6, 8, and 12, which is 24. The rates become plus 4, plus 3, minus 2 units per hour on a 24-unit tank. Net is 4 plus 3 minus 2, which is 5 units per hour. Time to fill is 24 divided by 5, so 4.8 hours. One division, no panic.

The fraction-filled-per-hour view is the same idea without the LCM. Each hour, the tank gains its net rate as a fraction of itself. If you ever need the level at a checkpoint, multiply net rate by elapsed hours. That is how the harder questions, where a pipe opens late or closes early, stay simple. You are always tracking one number: how much of the tank exists right now.

Solved questions 1 to 4: the basics

These four fix the foundation: two fillers, a filler against a drainer, multiple pipes, and a litres-based tank. Every answer below has been computed and checked.

Notice question 4 never touched a fraction. When the data is litres and a capacity, stay in litres. Matching your unit to the question is half the speed gain on this topic.

Solved questions 5 to 8: drainers and leaks

Here the drainer earns its keep. Late-opening drains, three signed pipes at once, hidden leaks, and a capacity tank with a drain all live in this group.

Question 7 is the leak template CAT loves. The leak is an invisible drainer, so you find its rate by subtracting the observed slow rate from the clean pipe rate, then invert. The same subtraction logic shows up whenever a tank underperforms its stated pipe.

Solved questions 9 to 12: mixed timing

The hardest group mixes partial fills, rotating pipes, a tank that starts part-full, and a back-solved drain. The fraction-per-hour view does the heavy lifting in every one.

Question 10 is the rotation classic. You do not simulate every hour; you find the net gain per cycle, count whole cycles, then walk only the final partial hour by hand. Question 11 is the sign-check question in pure form: compute the net first, read its sign, and let the sign tell you whether you are filling or emptying before you touch the time.

What to remember

Pipes and cisterns is one rule wearing many costumes: sign every pipe, add the signed rates into a net, and divide. The drainer is the only twist time and work does not have, and the sign convention tames it completely. Build the habit of checking the net's sign before you compute time, and the trick questions stop being tricky.

Drill the topic until the signs come automatically, then connect it to the wider rate family. The same logic that powers pipes also runs HCF and LCM tricks, since picking the tank as an LCM is what keeps your rates whole. When you want to see how a sharper Quant section moves your percentile, run your latest mock through the CAT score predictor and check the gap that pipes, work, and streams together can close on the CAT exam.

Common questions on pipes and cisterns