Pipes and Cisterns Questions for Placement (with Solutions)

Last Updated: March 2026

Pipes and Cisterns problems involve calculating the time taken to fill or empty a tank using multiple pipes. This topic is closely related to Time and Work. This guide provides 30 practice questions with detailed solutions.

Key Concepts and Formulas

Basic Definitions

Inlet: Pipe that fills the tank
Outlet: Pipe that empties the tank (also called leak)

Fundamental Formula

If a pipe can fill/empty a tank in n hours:

Part filled/emptied in 1 hour = 1/n

Working Together

If one pipe fills in x hours and another fills in y hours:

Part filled by both in 1 hour = 1/x + 1/y
Time to fill together = xy/(x+y)

Filling and Emptying Together

If pipe A fills in x hours and pipe B empties in y hours:

Net part filled in 1 hour = 1/x - 1/y
Time to fill = xy/(y-x) [when y > x]

Important Rules

If multiple pipes work together, add their rates
Inlets have positive rates, outlets have negative rates
Capacity is usually taken as LCM of individual times for easy calculation

30 Practice Questions with Solutions

Level 1: Basic (Questions 1-10)

Q1. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both pipes are used together, how long will it take to fill the tank?

Solution: Part filled by A in 1 min = 1/20 Part filled by B in 1 min = 1/30

Part filled by both in 1 min = 1/20 + 1/30 = (3+2)/60 = 5/60 = 1/12

Time taken = 12 minutes

Q2. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

Solution: One tap fills half tank in 3 hours

Four taps together fill at rate = 4 × (1/6) = 2/3 per hour

Time to fill remaining half = (1/2) ÷ (2/3) = 3/4 hour = 45 minutes

Total time = 3 hours + 45 minutes = 3 hours 45 minutes

Q3. A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both taps are opened simultaneously, after how much time will the cistern get filled?

Solution: Net part filled in 1 hour = 1/4 - 1/9 = (9-4)/36 = 5/36

Time to fill = 36/5 = 7.2 hours = 7 hours 12 minutes

Q4. A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both pipes are open, how long will it take to empty or fill the tank completely?

Solution: Net part emptied in 1 min = 1/6 - 1/10 = (5-3)/30 = 2/30 = 1/15

Since emptying is faster, tank will be emptied.

2/5 tank needs to be emptied Time = (2/5) ÷ (1/15) = (2/5) × 15 = 6 minutes

Q5. Two pipes A and B can fill a cistern in 37½ minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if pipe B is turned off after:

Solution: Let B be turned off after x minutes

A works for 30 minutes, B works for x minutes

Part filled = 30/(75/2) + x/45 = 1 60/75 + x/45 = 1 4/5 + x/45 = 1 x/45 = 1/5 x = 9

Q6. Three pipes A, B and C can fill a tank in 6 hours. After working together for 2 hours, C is closed and A and B fill the remaining part in 7 hours. How many hours will C alone take to fill the tank?

Solution: Part filled by A, B, C in 2 hours = 2/6 = 1/3 Remaining = 2/3

A and B fill 2/3 in 7 hours So A and B fill whole tank in 7 × 3/2 = 21/2 hours

1/C = 1/6 - 2/21 = (7-4)/42 = 3/42 = 1/14

Q7. Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all pipes are open, in how many hours will the tank be filled?

Solution: Part filled in 1 hour = 1/5 + 1/10 + 1/30 = (6 + 3 + 1)/30 = 10/30 = 1/3

Time = 3 hours

Q8. Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All three pipes working together can fill the tank in 15 minutes. What is the capacity of the tank?

Solution: Work done by waste pipe in 1 min = 1/15 - (1/20 + 1/24) = 1/15 - (6+5)/120 = 1/15 - 11/120 = (8-11)/120 = -3/120 = -1/40

Waste pipe empties 1/40 tank per minute Given it empties 3 gallons per minute

Capacity = 3 × 40 = 120 gallons

Q9. Two pipes A and B can fill a cistern in 12 minutes and 15 minutes respectively while a third pipe C can empty the full tank in 6 minutes. A and B are kept open for 5 minutes in the beginning and then C is also opened. In what time is the cistern emptied?

Solution: Part filled in 5 minutes = 5 × (1/12 + 1/15) = 5 × (5+4)/60 = 5 × 9/60 = 3/4

Net part emptied when all open = 1/6 - 1/12 - 1/15 = (10 - 5 - 4)/60 = 1/60 per minute

Time to empty 3/4 tank = (3/4) ÷ (1/60) = (3/4) × 60 = 45 minutes

Q10. A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold?

Solution: Work done by inlet in 1 hour = 1/8 + 1/12 = (3+2)/24 = 5/24

Inlet fills 5/24 tank per hour Given inlet fills 6 × 60 = 360 litres per hour

Capacity = 360 × 24/5 = 360 × 4.8 = 1728 litres

Level 2: Moderate (Questions 11-20)

Q11. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:

Solution: Let slower pipe fill in x minutes Faster pipe fills in x/3 minutes

1/x + 3/x = 1/36 4/x = 1/36 x = 144

Q12. A tank is filled in 5 hours by three pipes A, B and C. Pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

Solution: Let A's rate = x, then B = 2x, C = 4x

x + 2x + 4x = 1/5 7x = 1/5 x = 1/35

Time for A = 35 hours

Q13. 12 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?

Solution: Tank capacity = 12 × 13.5 = 162 litres

Number of 9-litre buckets = 162/9 = 18 buckets

Q14. Bucket P has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the empty drum. How many turns will it take for both buckets P and Q, having each turn together to fill the empty drum?

Solution: Let Q's capacity = 1 unit, then P's capacity = 3 units Drum capacity = 60 × 3 = 180 units

Together per turn = 3 + 1 = 4 units Number of turns = 180/4 = 45 turns

Q15. Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time can the third pipe alone empty the cistern?

Solution: Work done by third pipe in 1 min = 1/60 + 1/75 - 1/50 = (5 + 4 - 6)/300 = 3/300 = 1/100

Third pipe can empty in 100 minutes

Q16. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?

Solution: Part filled in 1 hour = 1/36 + 1/45 = (5+4)/180 = 9/180 = 1/20

Time = 20 hours

Q17. A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all three are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty the full cistern?

Solution: Work done by waste pipe = 1/12 + 1/15 - 1/20 = (5 + 4 - 3)/60 = 6/60 = 1/10

Waste pipe empties in 10 minutes

Q18. Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours will the tank be full?

Solution: In 2 hours (A then B): 1/6 + 1/4 = (2+3)/12 = 5/12 filled

After 4 hours (2 cycles): 10/12 = 5/6 filled Remaining = 1/6

5th hour: A opens, fills 1/6 Tank full in 5 hours

Q19. A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?

Solution: Let total time = x minutes

B works for x/2 minutes, fills (x/2)/40 = x/80 A and B together work for x/2 minutes, fills (x/2) × (1/60 + 1/40) = (x/2) × (5/120) = x/48

Total: x/80 + x/48 = 1 (3x + 5x)/240 = 1 8x = 240 x = 30

Q20. A tap can fill a tank in 16 hours whereas another tap can empty the tank in 8 hours. If in a three-fourths filled tank both the taps are opened, then how long will it take to empty the tank?

Solution: Net part emptied in 1 hour = 1/8 - 1/16 = (2-1)/16 = 1/16

3/4 tank to empty Time = (3/4) ÷ (1/16) = (3/4) × 16 = 12 hours

Level 3: Advanced (Questions 21-30)

Q21. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in:

Solution: A's rate = 1/12 per hour

First 2 hours (A+B, then A+C): Hour 1 (A+B): 1/12 + 1/15 = (5+4)/60 = 9/60 = 3/20 Hour 2 (A+C): 1/12 + 1/20 = (5+3)/60 = 8/60 = 2/15

In 2 hours: 3/20 + 2/15 = (9+8)/60 = 17/60

After 6 hours (3 cycles): 51/60 = 17/20 filled Remaining = 3/20

7th hour: A+B open, fills 3/20 in 1 hour

Total time = 7 hours

Q22. A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 m³. The emptying capacity of the tank is 10 m³ per minute higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?

Solution: Let filling capacity = x m³/min Emptying capacity = (x + 10) m³/min

Time to fill = 2400/x Time to empty = 2400/(x+10)

2400/x - 2400/(x+10) = 8 2400[(x+10-x)/(x(x+10))] = 8 2400 × 10 = 8x(x+10) 3000 = x² + 10x x² + 10x - 3000 = 0 (x + 60)(x - 50) = 0 x = 50

Q23. Two pipes A and B can fill a cistern in 10 and 15 minutes respectively. Both fill pipes are opened together, but at the end of 3 minutes, 'B' is turned off. How much time will the cistern take to fill?

Solution: Part filled in 3 minutes = 3 × (1/10 + 1/15) = 3 × (3+2)/30 = 3 × 5/30 = 1/2

Remaining = 1/2 A alone fills 1/2 at rate 1/10 per minute Time = (1/2) ÷ (1/10) = 5 minutes

Total time = 3 + 5 = 8 minutes

Q24. Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

Solution: Let A fill in x hours, then B fills in (x+6) hours

1/x + 1/(x+6) = 1/4 [(x+6+x)/(x(x+6))] = 1/4 (2x+6) × 4 = x(x+6) 8x + 24 = x² + 6x x² - 2x - 24 = 0 (x - 6)(x + 4) = 0 x = 6

Q25. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?

Solution: Part filled in 3 minutes = 3 × (1/30 + 1/20 + 1/10) = 3 × (2 + 3 + 6)/60 = 3 × 11/60 = 11/20

Part filled by C in 3 minutes = 3/10 = 6/20

Proportion of R = (6/20) ÷ (11/20) = 6/11

Q26. Two pipes can fill a tank in 25 and 30 minutes respectively and a waste pipe can empty 3 gallons per minute. All three pipes working together can fill the tank in 15 minutes. What is the capacity of the tank?

Solution: Work done by waste pipe = 1/15 - (1/25 + 1/30) = 1/15 - (6+5)/150 = 1/15 - 11/150 = (10-11)/150 = -1/150

Waste pipe empties 1/150 tank per minute Given: 3 gallons per minute

Capacity = 3 × 150 = 450 gallons

Q27. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?

Solution: Part filled in 1 hour = 1/36 + 1/45 = (5+4)/180 = 9/180 = 1/20

Time = 20 hours

Q28. A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. What is the time required by the first pipe?

Solution: Let first pipe fill in x hours Second pipe = (x-5) hours Third pipe = (x-5-4) = (x-9) hours

First two together = third alone 1/x + 1/(x-5) = 1/(x-9) [(x-5+x)/(x(x-5))] = 1/(x-9) (2x-5)(x-9) = x(x-5) 2x² - 18x - 5x + 45 = x² - 5x x² - 18x + 45 = 0 (x-15)(x-3) = 0

x = 15 (x = 3 gives negative time for third pipe)

Q29. 12 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?

Solution: Tank capacity = 12 × 13.5 = 162 litres

Buckets needed = 162/9 = 18 buckets

Q30. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?

Solution: Part filled in 4 minutes = 4 × (1/15 + 1/20) = 4 × (4+3)/60 = 4 × 7/60 = 7/15

Remaining = 8/15

B fills 8/15 at rate 1/20 per minute Time = (8/15) ÷ (1/20) = (8/15) × 20 = 32/3 = 10⅔ minutes

Total time = 4 + 10⅔ = 14⅔ minutes = 14 minutes 40 seconds

Shortcuts and Tricks

Trick 1: LCM Method for Quick Calculation

Take LCM of individual times as tank capacity, then work in units.

Example: Pipes in 20 and 30 min LCM = 60 units Pipe A fills 3 units/min, Pipe B fills 2 units/min Together: 5 units/min → 60/5 = 12 minutes

Trick 2: Harmonic Mean for Two Pipes

Time together = (t1 × t2)/(t1 + t2)

Trick 3: Net Rate Formula

When filling and emptying together: Net time = (f × e)/(e - f) where e > f

Trick 4: Alternating Pipes

Calculate work done in complete cycles, then remaining work.

Trick 5: Partial Work Problems

Always calculate work done in the first phase, then remaining work.

Companies Testing This Topic

Company	Frequency	Difficulty
TCS	Frequently asked	Easy-Medium
Infosys	Common	Easy
Wipro	Common	Easy
Cognizant	Frequently asked	Easy
Accenture	Common	Easy-Medium
Capgemini	Common	Easy
HCL	Sometimes	Medium

Frequently Asked Questions (FAQ)

Q1: Are Pipes and Cisterns questions similar to Time and Work?

A: Yes, they follow the same principles. The tank capacity is analogous to total work, and pipe rates correspond to worker efficiencies. If you understand Time and Work, Pipes and Cisterns will be easy.

Q2: What is the most efficient method to solve these problems?

A: The LCM method is fastest for most problems. Take LCM of all time values as tank capacity, convert to units per hour/minute, then solve. Avoid fractions when possible.

Q3: How do I handle problems with pipes opening at different times?

A: Break into phases. Calculate work done by pipes that are open, then remaining work for pipes that continue. Always track who is open when.

Q4: Can these problems have negative answers?

A: No, time cannot be negative. If you get negative time, check your setup. Usually means you assumed filling when it's actually emptying or vice versa.

Q5: What are the most common trap answers?

A: Watch for: forgetting to add time when pipes work sequentially, mixing up filling and emptying rates, and incorrect unit conversions (hours to minutes).

Practice these patterns and you'll master Pipes and Cisterns!

Pipes And Cisterns Questions Placement