PIPES & CISTERN

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Pipes and Cistern

Inlet:

A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.

Outlet:

A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.

If a pipe can fill a tank in xhours, then:

part filled in 1 hour =	1	.
	x

If a pipe can empty a tank in yhours, then:

part emptied in 1 hour =	1	.
	y

If a pipe can fill a tank in xhours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then

the net part filled in 1 hour =		1	–	1		.
		x		y

If a pipe can fill a tank in xhours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes, then

the net part emptied in 1 hour =		1	–	1		.
		y		x

Questions:

Level-I:

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 the 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?

Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:

1	13	hours
	17

2	8	hours
	11

3	9	hours
	17

4	1	hours
	2

A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in:

4	1	hours
	3

7 hours

8 hours

14 hours

Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:

A.	5 min.
B.	9 min.
C.	10 min.
D.	15 min.

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. The time required by the first pipe is:

A.	6 hours
B.	10 hours
C.	15 hours
D.	30 hours

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

A.	60 gallons
B.	100 gallons
C.	120 gallons
D.	180 gallons

A tank is filled in 5 hours by three pipes A, B and C. The 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?

A.	20 hours
B.	25 hours
C.	35 hours
D.	Cannot be determined
E.	None of these

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?

A.	1 hour
B.	2 hours
C.	6 hours
D.	8 hours

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

A.	12 min
B.	15 min
C.	25 min
D.	50 min

10.

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

A.	10 min. 20 sec.
B.	11 min. 45 sec.
C.	12 min. 30 sec.
D.	14 min. 40 sec.

11.

Level-II:

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:

A.	81 min.
B.	108 min.
C.	144 min.
D.	192 min.

12.

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?

A.	15 min
B.	20 min
C.	27.5 min
D.	30 min

13.

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?

A.	3 hrs 15 min
B.	3 hrs 45 min
C.	4 hrs
D.	4 hrs 15 min

14.

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:

6 hours

6	2	hours
	3

7 hours

7	1	hours
	2

15.

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:

A.	10
B.	12
C.	14
D.	16

16.

How much time will the leak take to empty the full cistern?
I.	The cistern is normally filled in 9 hours.
II.	It takes one hour more than the usual time to fill the cistern because of la leak in the bottom.

A.	I alone sufficient while II alone not sufficient to answer
B.	II alone sufficient while I alone not sufficient to answer
C.	Either I or II alone sufficient to answer
D.	Both I and II are not sufficient to answer
E.	Both I and II are necessary to answer

17.

How long will it take to empty the tank if both the inlet pipe A and the outlet pipe B are opened simultaneously?
I.	A can fill the tank in 16 minutes.
II.	B can empty the full tank in 8 minutes.

A.	I alone sufficient while II alone not sufficient to answer
B.	II alone sufficient while I alone not sufficient to answer
C.	Either I or II alone sufficient to answer
D.	Both I and II are not sufficient to answer
E.	Both I and II are necessary to answer

18.

If both the pipes are opened, how many hours will be taken to fill the tank?
I.	The capacity of the tank is 400 litres.
II.	The pipe A fills the tank in 4 hours.
III.	The pipe B fills the tank in 6 hours.

A.	Only I and II
B.	Only II and III
C.	All I, II and III
D.	Any two of the three
E.	Even with all the three statements, answer cannot be given.

Answers:

Level-I:

Answer:1 Option B

Explanation:

Part filled by (A + B + C) in 3 minutes = 3		1	+	1	+	1		=		3 x	11		=	11	.
		30		20		10					60			20

Part filled by C in 3 minutes =	3	.
	10

Required ratio =		3	x	20		=	6	.
		10		11			11

Answer:2 Option C

Explanation:

Net part filled in 1 hour		1	+	1	–	1		=	17	.
		5		6		12			60

The tank will be full in	60	hours i.e., 3	9	hours.
	17		17

Answer:3 Option D

Explanation:

Work done by the leak in 1 hour =		1	–	3		=	1	.
		2		7			14

Leak will empty the tank in 14 hrs.

Answer:4 Option B

Explanation:

Let B be turned off after x minutes. Then,

Part filled by (A + B) in x min. + Part filled by A in (30 –x) min. = 1.

x		2	+	1		+ (30 – x).	2	= 1
		75		45			75

	11x	+	(60 -2x)	= 1
	225		75

11x + 180 – 6x = 225.

x = 9.

Answer:5 Option C

Explanation:

Suppose, first pipe alone takes x hours to fill the tank .

Then, second and third pipes will take (x -5) and (x – 9) hours respectively to fill the tank.

	1	+	1	=	1
	x		(x – 5)		(x – 9)

	x – 5 + x	=	1
	x(x – 5)		(x – 9)

(2x – 5)(x – 9) = x(x – 5)

x² – 18x + 45 = 0

(x – 15)(x – 3) = 0

x = 15. [neglecting x = 3]

Answer:6 Option C

Explanation:

Work done by the waste pipe in 1 minute =	1	–		1	+	1
	15			20		24

=		1	–	11
		15		120

= –	1	. [-ve sign means emptying]
	40

Volume of	1	part = 3 gallons.
	40

Volume of whole = (3 x 40) gallons = 120 gallon

Answer:7 Option C

Explanation:

Suppose pipe A alone takes x hours to fill the tank.

Then, pipes B and C will take	x	and	x	hours respectively to fill the tank.
	2		4

	1	+	2	+	4	=	1
	x		x		x		5

	7	=	1
	x		5

x = 35 hrs.

Answer:8 Option C

Explanation:

Let the cistern be filled by pipe A alone in x hours.

Then, pipe B will fill it in (x + 6) hours.

	1	+	1	=	1
	x		(x + 6)		4

	x + 6 + x	=	1
	x(x + 6)		4

x² – 2x – 24 = 0

(x -6)(x + 4) = 0

x = 6. [neglecting the negative value of x]

Answer:9 Option A

Explanation:

Part filled by A in 1 min =	1	.
	20

Part filled by B in 1 min =	1	.
	30

Part filled by (A + B) in 1 min =		1	+	1		=	1	.
		20		30			12

Both pipes can fill the tank in 12 minutes.

Answer:10 Option D

Explanation:

Part filled in 4 minutes = 4		1	+	1		=	7	.
		15		20			15

Remaining part =		1 –	7		=	8	.
			15			15

Part filled by B in 1 minute =	1
	20

	1	:	8	:: 1 : x
	20		15

x =		8	x 1 x 20		= 10	2	min = 10 min. 40 sec.
		15				3

The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.

Level-II:

Answer:11 Option C

Explanation:

Let the slower pipe alone fill the tank in x minutes.

Then, faster pipe will fill it in	x	minutes.
	3

	1	+	3	=	1
	x		x		36

	4	=	1
	x		36

x = 144 min.

Answer:12 Option D

Explanation:

Part filled by (A + B) in 1 minute =		1	+	1		=	1	.
		60		40			24

Suppose the tank is filled in x minutes.

Then,	x		1	+	1		= 1
	2		24		40

	x	x	1	= 1
	2		15

x = 30 min.

Answer:13 Option B

Explanation:

Time taken by one tap to fill half of the tank = 3 hrs.

Part filled by the four taps in 1 hour =		4 x	1		=	2	.
			6			3

Remaining part =		1 –	1		=	1	.
			2			2

	2	:	1	:: 1 : x
	3		2

x =		1	x 1 x	3		=	3	hours i.e., 45 mins.
		2		2			4

So, total time taken = 3 hrs. 45 mins.

Answer:14 Option C

Explanation:

(A + B)’s 1 hour’s work =		1	+	1		=	9	=	3	.
		12		15			60		20

(A + C)’s hour’s work =		1	+	1		=	8	=	2	.
		12		20			60		15

Part filled in 2 hrs =		3	+	2		=	17	.
		20		15			60

Part filled in 6 hrs =		3 x	17		=	17	.
			60			20

Remaining part =		1 –	17		=	3	.
			20			20

Now, it is the turn of A and B and	3	part is filled by A and B in 1 hour.
	20

Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.

Answer:15 Option C

Explanation:

Part filled in 2 hours =	2	=	1
	6		3

Remaining part =		1 –	1		=	2	.
			3			3

(A + B)’s 7 hour’s work =	2
	3

(A + B)’s 1 hour’s work =	2
	21

C’s 1 hour’s work = { (A + B + C)’s 1 hour’s work } – { (A + B)’s 1 hour’s work }

=		1	–	2		=	1
		6		21			14

C alone can fill the tank in 14 hours.

Answer:16 Option E

Explanation:

Time taken to fill the cistern without leak = 9 hours.

Part of cistern filled without leak in 1 hour =	1
	9

Time taken to fill the cistern in presence of leak = 10 hours.

Net filling in 1 hour =	1
	10

Work done by leak in 1 hour =		1	–	1		=	1
		9		10			90

Leak will empty the full cistern in 90 hours.

Clearly, both I and II are necessary to answer the question.

Correct answer is (E).

Answer:17 Option E

Explanation:

I. A’s 1 minute’s filling work =	1
	16

II. B’s 1 minute’s filling work =	1
	8

(A + B)’s 1 minute’s emptying work =		1	–	1		=	1
		8		16			16

Tank will be emptied in 16 minutes.

Thus, both I and II are necessary to answer the question.

Correct answer is (E).

Answer:18 Option B

Explanation:

II. Part of the tank filled by A in 1 hour =	1
	4

III. Part of the tank filled by B in 1 hour =	1
	6

(A + B)’s 1 hour’s work =		1	+	1		=	5
		4		6			12

A and B will fill the tank in	12	hrs = 2 hrs 24 min.
	5

So, II and III are needed.

Correct answer is (B).,

Pipes and Cisterns

Pipes and cisterns are essential components of any water system. Pipes transport water from its source to its destination, while cisterns store water for later use.

Aqueduct

An aqueduct is a man-made structure that carries water over a long distance. Aqueducts are typically built using stone, brick, or concrete, and they can be either above or below ground. The earliest aqueducts were built in ancient Greece and Rome, and they were used to transport water from rivers and springs to cities. Aqueducts are still in use today, and they are an important part of many water systems.

Cistern

A cistern is a container that stores water. Cisterns can be made of a variety of materials, including stone, brick, concrete, and Metal. They can be either above or below ground, and they can be either open or closed. Cisterns are used to store water for a variety of purposes, including drinking, bathing, and Irrigation.

Conduit

A conduit is a tube or pipe that carries water or other fluids. Conduits are typically made of metal, plastic, or concrete, and they can be either above or below ground. Conduits are used to transport water, sewage, and other fluids from one location to another.

Culvert

A culvert is a small tunnel that carries water under a road or other obstacle. Culverts are typically made of concrete or metal, and they can be either round or rectangular in shape. Culverts are used to prevent flooding and to protect roads and other Infrastructure-2/”>INFRASTRUCTURE from damage caused by water.

Drain

A drain is a pipe or channel that carries wastewater away from a building or other structure. Drains are typically made of PVC, ABS, or cast iron, and they can be either above or below ground. Drains are used to prevent flooding and to protect buildings and other structures from damage caused by water.

Flume

A flume is a channel that carries water over a long distance. Flumes are typically made of wood, concrete, or metal, and they can be either open or closed. Flumes are used to transport water from rivers and streams to irrigation systems and other water users.

Gutter

A gutter is a channel that carries rainwater away from a building or other structure. Gutters are typically made of aluminum, steel, or PVC, and they are installed along the edges of roofs. Gutters are used to prevent water from damaging the foundation of a building and to prevent flooding.

Pipe

A pipe is a tube that carries water or other fluids. Pipes are typically made of metal, plastic, or concrete, and they can be either above or below ground. Pipes are used to transport water, sewage, and other fluids from one location to another.

Sewer

A sewer is a pipe or tunnel that carries wastewater away from a building or other structure. Sewers are typically made of concrete or PVC, and they can be either above or below ground. Sewers are used to collect and transport wastewater to treatment Plants.

Siphon

A siphon is a device that uses the principle of Atmospheric Pressure to transport liquids from one location to another. Siphons are typically made of glass, plastic, or metal, and they can be either above or below ground. Siphons are used to transport water, sewage, and other fluids from one location to another.

Storm drain

A storm drain is a pipe or channel that carries rainwater away from a building or other structure. Storm drains are typically made of concrete or PVC, and they are installed along the edges of roads and sidewalks. Storm drains are used to prevent flooding and to protect roads and other infrastructure from damage caused by water.

Water main

A water main is a large pipe that carries water from a water treatment plant to homes and businesses. Water mains are typically made of steel or cast iron, and they are buried underground. Water mains are used to provide a reliable source of water for drinking, bathing, and other purposes.

Water tank

A water tank is a container that stores water. Water tanks can be made of a variety of materials, including steel, concrete, and fiberglass. They can be either above or below ground, and they can be either open or closed. Water tanks are used to store water for a variety of purposes, including drinking, bathing, and irrigation.

What is a pipe?

A pipe is a hollow tube that is used to transport fluids or gases. Pipes are typically made of metal, plastic, or concrete, and they can be either rigid or flexible.

What is a cistern?

A cistern is a container that is used to store water. Cisterns are typically made of concrete, metal, or plastic, and they can be either above-ground or below-ground.

What are the different types of pipes?

There are many different types of pipes, including:

Water pipes: These pipes are used to transport water for drinking, bathing, and other purposes.
Sewer pipes: These pipes are used to transport wastewater away from homes and businesses.
Gas pipes: These pipes are used to transport natural gas to homes and businesses.
Oil pipes: These pipes are used to transport oil from oil fields to refineries.

What are the different types of cisterns?

There are many different types of cisterns, including:

Above-ground cisterns: These cisterns are located above ground, and they are typically made of concrete or metal.
Below-ground cisterns: These cisterns are located below ground, and they are typically made of concrete or plastic.
Rainwater cisterns: These cisterns are used to collect rainwater, and they are typically made of concrete or plastic.
Graywater cisterns: These cisterns are used to collect graywater, which is wastewater from sinks, showers, and washing machines.

What are the benefits of using pipes?

There are many benefits of using pipes, including:

Pipes are a very efficient way to transport fluids and gases.
Pipes are relatively inexpensive to install and maintain.
Pipes are available in a variety of materials, which makes them suitable for a variety of applications.

What are the benefits of using cisterns?

There are many benefits of using cisterns, including:

Cisterns can provide a reliable source of water during emergencies.
Cisterns can help to reduce water bills.
Cisterns can help to conserve water.
Cisterns can help to improve water quality.

What are the disadvantages of using pipes?

There are a few disadvantages of using pipes, including:

Pipes can be damaged by leaks or breaks.
Pipes can be a breeding ground for bacteria.
Pipes can be expensive to repair or replace.

What are the disadvantages of using cisterns?

There are a few disadvantages of using cisterns, including:

Cisterns can be expensive to install.
Cisterns can take up a lot of space.
Cisterns can be difficult to maintain.
Cisterns can be a breeding ground for mosquitoes.

How are pipes and cisterns used?

Pipes and cisterns are used in a variety of applications, including:

Water supply: Pipes are used to transport water from water treatment plants to homes and businesses.
Sewerage: Pipes are used to transport wastewater from homes and businesses to sewage treatment plants.
Gas supply: Pipes are used to transport natural gas from gas wells to homes and businesses.
Oil transportation: Pipes are used to transport oil from oil fields to refineries.
Rainwater harvesting: Cisterns are used to collect rainwater, which can then be used for watering plants, washing cars, or flushing toilets.
Graywater recycling: Cisterns are used to collect graywater, which can then be used for watering plants or flushing toilets.

What are the safety precautions that should be taken when using pipes and cisterns?

When using pipes and cisterns, it is important to take the following safety precautions:

Always use the proper tools and equipment when working with pipes and cisterns.
Always follow the manufacturer’s instructions when installing or maintaining pipes and cisterns.
Never work with pipes or cisterns that are damaged or leaking.
Always wear safety gear when working with pipes or cisterns, such as gloves, goggles, and a hard hat.

What are the environmental impacts of using pipes and cisterns?

The environmental impacts of using pipes and cisterns vary depending on the materials used, the type of application, and the location of the pipes or cisterns. In general, however, pipes and cisterns can have a positive impact on the Environment by reducing water waste and improving water quality.

Sure, here are some MCQs without mentioning the topic PIPES & CISTERN:

A liquid flows through a pipe at a rate of 10 liters per second. The pipe has a diameter of 10 cm. What is the velocity of the liquid in the pipe?
A water tank has a capacity of 1000 liters. The tank is filled with water at a rate of 10 liters per minute. How long will it take to fill the tank?
A water pipe has a diameter of 5 cm. The water pressure in the pipe is 100 kPa. What is the flow rate of water in the pipe?
A water tank has a height of 10 m. The tank is filled with water at a rate of 10 liters per second. What is the pressure of the water at the bottom of the tank?
A water pipe has a length of 100 m. The water pressure in the pipe is 100 kPa. What is the head loss in the pipe?

Answers:
1. 100 cm/s
2. 100 minutes
3. 200 liters per second
4. 100 kPa
5. 10 m