Pipes and Cisterns Tricks

📑 On this page

⚡ The short answer

A pipe that fills a tank in n hours fills 1/n of it per hour. Inlets add, leaks and outlets subtract, and time = 1 ÷ net rate. Faster: call the tank the LCM of the times so every rate is a whole number. The trap: rates add and subtract, times never do.

🎬 The 30-second story

The terrace tank that would not fill

“The new motor fills our terrace tank in 4 hours flat.”

🏠

Rohan

Rohan switches it on.

“Wait. There's a crack at the bottom. It's dripping.”

💧

Rohan

The crack would empty a full tank in 12 hours.

“Easy. 12 minus 4. It'll be full in 8 hours.”

🧮

Aarav

Aarav subtracts the times.

“It took 6. Your maths owes me two hours of sleep.”

⏰

Rohan

The tank disagrees.

Tara's maths: Times don't subtract; work per hour does. Call the tank 12 buckets (LCM of 4 and 12). The motor pours 3 buckets an hour, the crack loses 1. Net: 2 buckets an hour, so 12 ÷ 2 = 6 hours.

What are pipes and cisterns, really?

A cistern is just a tank. Inlets fill it, outlets and leaks empty it. The real question: how fast is the level moving? If you know time and work, you know this chapter. A pipe is a worker who never takes chai breaks; a leak is one who undoes the job.

⚔️ Side by side

Same maths, different costume

👷Time and work

people finishing a job

•10 days alone: 1/10 a day

🚰Pipes and cisterns

pipes filling a tank

•10 hours alone: 1/10 an hour

Test	Time and work	Pipes and cisterns
Negative work	Rare	Common (leaks, outlets)
Can it go on forever?	No	Yes, if outlets win

The only new idea is the minus sign.

Why rates, not times? A pipe that takes twice as long is half as fast: time and rate are inversely related, so times can't be added. Convert to "how much per hour" first, and everything adds like pocket money.

What is the formula for pipes and cisterns, and why does it work?

🧮 The formula

Net rate: the only formula you need

🚰

1/a

inlet A

🚰

1/b

inlet B

🕳️

− 1/c

outlet C

⏱️

Time = 1 ÷ net rate

if net rate > 0

Fractions get messy with three pipes, so use the LCM tank. Inlets take 12 and 15 hours, an outlet 20: call the tank 60 units. Each pipe's hourly rate is now a whole number, 60 ÷ its time.

📊 The data

A 60-unit tank: units per hour

Inlet A (12 hrs)

5 units/hr

Inlet B (15 hrs)

4 units/hr

Outlet C (20 hrs) · subtract this

3 units/hr

Net: 5 + 4 − 3 · 60 ÷ 6 = 10 hours

6 units/hr

The units are imaginary; the answer is real. The LCM just keeps numbers small.

Situation	Shortcut	Example	Answer
Two inlets	xy ÷ (x + y)	20 and 30 min	12 min
Inlet x, outlet y (y > x)	xy ÷ (y − x)	4 and 12 hrs	6 hrs
Inlet alone x, with leak y	Leak empties in xy ÷ (y − x)	8 hrs, 10 hrs	40 hrs
Three or more pipes	LCM tank	12, 15, −20	10 hrs

→ scroll to see more

How do you solve pipes and cisterns questions step by step?

✍️ Worked example Warm-up ⏱ 30 sec

Two hoses, one aquarium

Meher fills her aquarium with two hoses. One alone takes 20 minutes, the other 30. With both running, how long?

1
LCM of 20 and 30 = 60 units.
2
Hose 1: 3 units a minute. Hose 2: 2 units a minute.
3
Together: 5 units a minute. Time = 60 ÷ 5 = 12 minutes.

Answer: 12 minutes

⚡ Product over sum

20 × 30 ÷ 50 = 12. It must be less than 20, the faster hose alone.

✍️ Worked example CLAT level ⏱ 45 sec

Two inlets fighting one outlet

Kabir's rooftop tank: inlet A fills it in 12 hours, inlet B in 15, and the outlet to his shop empties it in 20. All three open on an empty tank. When is it full?

1
LCM of 12, 15 and 20 = 60 units.
2
A: +5 an hour. B: +4 an hour. Outlet: −3 an hour.
3
Net = 5 + 4 − 3 = 6 units an hour.
4
Time = 60 ÷ 6 = 10 hours.

Answer: 10 hours

⚡ The exam-hall shortcut

Bracket first. A and B alone take 60 ÷ 9 ≈ 6.7 hours; the outlet only slows them, so any option below 6.7 is dead.

✍️ Worked example CLAT level ⏱ 40 sec

Find the leak

Rohan's purifier tank normally fills in 8 hours. A leak makes it take 10. How long would the leak alone take to empty a full tank?

1
LCM of 8 and 10 = 40 units.
2
Inlet alone: 40 ÷ 8 = 5 units an hour.
3
Inlet with leak: 40 ÷ 10 = 4 units an hour.
4
So the leak steals 5 − 4 = 1 unit an hour. It empties 40 units in 40 hours.

Answer: 40 hours

⚡ The exam-hall shortcut

xy ÷ (y − x) = 8 × 10 ÷ 2 = 40.

✍️ Worked example Tricky ⏱ 60 sec

One pipe shut midway

For the college fest, Zoya fills a drum with pipe A (18 hours alone) and pipe B (24 hours alone). After 6 hours together, A is moved to the kitchen. How long does the drum take in total?

1
LCM of 18 and 24 = 72 units. A: 4 an hour, B: 3 an hour.
2
6 hours together: 6 × 7 = 42 units.
3
Left: 72 − 42 = 30 units, for B alone at 3 an hour = 10 more hours.
4
Total = 6 + 10 = 16 hours.

Answer: 16 hours in total (10 hours after A leaves)

⚡ The exam-hall shortcut

Chop time into blocks where the same pipes run; units = rate × time in each. Expect 10 hours as a trap option for "after A leaves".

What is the fastest way to crack pipes and cisterns?

✓LCM, unless there are exactly two pipes. Then product over sum (or difference) is quicker.
✓Bracket first. Inlets together beat the fastest single inlet; an outlet makes the answer bigger than the inlets-only time.
✓Ratios are rates. A twice as fast as B, together 12 hours: rates 2 : 1, tank 36 units, B alone 36 hours.
✓Never fills? If outlets drain at least as fast as inlets fill, the net rate is zero or negative.

🎛️ Try it yourself — change any number

Run your own fest water drum

Inlet A fills alone in (hours) Inlet B fills alone in (hours) Pipe C (negative = drain, 0 = closed)

Together

7.5

Work done per unit time

13.33%

1/10 + 1/15 − 1/30 = 0.1333 → 7.5

As set: 1/10 + 1/15 − 1/30 = 2/15, so 7.5 hours. Set C to 0: 6 hours. Set C to −5: the drain wins and it never fills.

Hours (decimal)	Fraction	Minutes
0.2	1/5	12 min
0.25	1/4	15 min
0.4	2/5	24 min
0.5	1/2	30 min
0.75	3/4	45 min
0.8	4/5	48 min

→ scroll to see more

⚠️ 4.8 hours is not 4 hours 80 minutes

Multiply the decimal part by 60: 0.8 × 60 = 48, so 4.8 hours = 4 hours 48 minutes. "5 hours 20 minutes" is planted for whoever reads 4.8 as 4 hours 80 minutes.

What happens when pipes open or close at different times?

Staggered starts, shut-offs and turns all use one idea: chop time into blocks and add the units. The classic trap: A fills in 4 hours, B in 6, and they run alternately, an hour each, A first. Tank = 12 units; A adds 3, B adds 2.

🕒 Timeline

A and B take turns on a 12-unit tank

A
Hour 1

A: +3 → 3 units

B waits.
B
Hour 2

B: +2 → 5 units

One full cycle = 5 units in 2 hours.
↻
Hours 3–4

Another cycle → 10 units

Only 2 units left.
A
Hour 5

A needs 2 of its 3 → 40 minutes

Total 4 hours 40 minutes, not 12 ÷ 2.5 = 4.8: A finishes mid-turn.

How do pipes and cisterns hide in a CLAT caselet?

CLAT now describes a housing society or water scheme in litres and clock times. Turn every sentence into litres per hour, with a sign. Say a society tank holds 3,600 litres.

📊 The data

Green Park society's 3,600-litre tank: litres per hour

Borewell pump (fills in 4 hrs)

900 L/hr

Municipal line (fills in 12 hrs)

300 L/hr

Residents' taps (drain in 9 hrs) · subtract

400 L/hr

Net with all three on · 3,600 ÷ 800 = 4.5 hours

800 L/hr

All on at 6 a.m.: full at 10:30 a.m. Forget the taps and you get 9 a.m., an option CLAT would plant.

🧭 Decision flow

Four checks before you touch a number

❓ Is every pipe described against the same full tank?

No →

Rescale first. "Fills half the tank in 3 hours" means the full tank in 6.

Yes ↓

❓ Is any pipe emptying, leaking or drawing water?

Yes →

Give it a minus sign, then go on to check the timing.

No ↓

❓ Do all pipes run for the whole time?

No →

Chop the timeline into blocks; add units block by block.

Yes ↓

❓ Does the question ask for litres, and is the capacity given?

Yes →

Net litres per hour × hours. Done.

No →

Litres without a capacity: cannot be determined. A fraction of the tank is all you can find.

⚠️ Where the marks leak

Averaging or subtracting times. Treating a drain as an inlet. Answering "after the pipe closes" when asked "in total". And missing that a stronger outlet means an empty tank never fills.

How CLAT asked it

📝 Asked in CLAT 2019 · Q57 Two fill, one empties

A tank is connected to three pipes – Pipe A, B and C. Pipe A can fill the tank in 6 hours, B can fill the tank in 8 hours and Pipe C can empty the full tank in 12 hours. How much time will it take to fill the tank completely if all three pipes are working together?

A4 hours

B4 hours 48 minutes

C5 hours

D5 hours 20 minutes

Reveal answer + reasoning

Answer: B

There is no official key for 2019; this is our solution. Tank = LCM 24 units. A: +4 an hour, B: +3, C: −2. Net = 5 units an hour, so 24 ÷ 5 = 4.8 hours = 4 hours 48 minutes. About 40 seconds.

Why the others fail

A — Drops the 0.8 hour.
C — Rounds 4.8 hours up to 5.
D — Reads 4.8 hours as 4 hours 80 minutes.

📝 Asked in CLAT 2018 · Q145 Pipes opened an hour apart

Four pipes A, B, C and D can fill a tank with water in 15, 20, 30 and 60 hours respectively. Pipe A is opened at 4 a.m., B at 5 a.m., C at 6 a.m. and D at 7 a.m. When is the tank filled up completely?

A9:30 a.m.

B10:00 a.m.

C10:30 a.m.

D11:00 a.m.

Reveal answer + reasoning

Answer: D

Tank = LCM 60; A 4, B 3, C 2, D 1 units an hour. Eliminate: all four from 4 a.m. would do 10 an hour and finish at 10 a.m.; late starts only delay, so A and B are out.
Blocks: 4–5 a.m. A: 4. 5–6 a.m. A + B: 7 (total 11). 6–7 a.m. A + B + C: 9 (total 20). From 7 a.m., 10 an hour clears the last 40 in 4 hours: 11:00 a.m. About 60 seconds.

Why the others fail

A — Earlier than even the all-at-4 a.m. finish. Impossible.
B — Assumes all four start together at 4 a.m.
C — A guess; the blocks give exactly 4 hours after 7 a.m.

💥 Myth vs fact

Myth vs fact

🙅 Myth

A 4-hour inlet and a 12-hour leak: 12 − 4 = 8 hours.

Tap to bust it →

✅ Fact

Subtract rates: 1/4 − 1/12 = 1/6, so 6 hours.

🙅 Myth

A tank with a leak can never fill.

Tap to bust it →

✅ Fact

It fills whenever inlets beat the leak.

🙅 Myth

Product over sum works for any number of pipes.

Tap to bust it →

✅ Fact

It is a two-pipe shortcut. For three or more, use the LCM tank.

🙅 Myth

Pipes taking turns: divide by the average rate.

Tap to bust it →

✅ Fact

The last pipe can finish mid-turn.

Can you do these five?

🎯 Quick quiz

Five pipes and cisterns checks

0 / 5

Two taps fill a hostel tank in 12 and 24 minutes.

Q1. With both open, how long does it take to fill?

An inlet fills a tank in 5 hours; an outlet empties it in 7.5. Both open on an empty tank.

Q2. How long until it is full?

A pipe usually fills a tank in 10 hours. Because of a leak, it now takes 12 hours.

Q3. How long would the leak alone take to empty the full tank?

Pipe A fills a tank in 20 minutes and pipe B in 30 minutes. Both start together, but B is shut after 6 minutes.

Q4. How long does it take, in total, to fill the tank?

Two inlets fill a tank in 6 and 9 hours. Both run for 2 hours on an empty tank. Capacity is not stated.

Q5. How many litres of water are in the tank now?

🎯 Pipes and cisterns in a nutshell

A pipe that fills a tank in n hours does 1/n an hour. Rates add; times never do.
Inlets plus, outlets minus. Time = 1 ÷ net rate.
Use the LCM tank to turn fractions into whole units.
Staggered pipes: chop time into blocks.
No capacity, no litres.

📎 Formula card

Rate: fills in n hours → +1/n per hour; empties in n hours → −1/n per hour
Time to fill: 1 ÷ (1/a + 1/b − 1/c)
Two inlets: xy ÷ (x + y)
Inlet x, outlet y (y > x): xy ÷ (y − x)
Leak alone (fill x hours, y with leak): xy ÷ (y − x)
LCM tank: rate = LCM ÷ the pipe's time
Hours to minutes: multiply the decimal part by 60 (0.8 hour = 48 min)

Frequently asked questions

What is the basic formula for pipes and cisterns?

A pipe that fills a tank in n hours fills 1/n of it every hour; one that empties it in n hours removes 1/n. Add the filling rates, subtract the emptying ones, and divide 1 by the net rate. A 4-hour inlet with a 12-hour leak: 1/4 − 1/12 = 1/6, so 6 hours.

What is the LCM method in pipes and cisterns?

Assume the tank holds the LCM of all the times, in imaginary units. Each pipe's hourly rate becomes a whole number. With inlets of 12 and 15 hours and a 20-hour outlet, the tank is 60 units, rates are 5, 4 and minus 3, the net is 6, and it fills in 10 hours.

How do you find how long a leak takes to empty a tank?

Compare the fill rate with and without the leak. A pipe taking 8 hours alone and 10 with a leak fills 1/8 and 1/10 an hour. The leak's rate is the difference, 1/40, so it empties the full tank in 40 hours. Shortcut: xy divided by (y minus x).

Is pipes and cisterns asked in CLAT?

Yes. CLAT 2019 asked two inlets and an outlet working together (4 hours 48 minutes). CLAT 2018 asked four pipes opened an hour apart (full at 11 a.m.). In today's caselet pattern, expect it as a rate question inside a paragraph about a tank or a water supply.

Why can't I just add or average the times of two pipes?

Because time and rate are inversely proportional: a slower pipe takes more time but adds less water per hour. Convert each time to a rate, add or subtract the rates, then flip back to time. Hoses of 20 and 30 minutes fill together in 12 minutes, not 25.