Pipes And Cistern

Question:
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

Answer: 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.

Question:
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.

Answer: 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.

Question:
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

Answer: 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 gallons.

Question:
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:

[A].

6 hours

[B].

6	2	hours
	3

[C].

7 hours

[D].

7	1	hours
	2

Answer: 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.

Question:
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.

Answer: 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.

Question:
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

Answer: 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]

Question:
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

Answer: 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]

Question: 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:
[A].

4	1	hours
	3

[B].

7 hours

[C].

8 hours

[D].

14 hours

Answer: 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.

Question:
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?

[A].

5

11

[B].

6

11

[C].

7

11

[D].

8

11

Answer: 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

Question:
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:

[A].

1	13	hours
	17

[B].

2	8	hours
	11

[C].

3	9	hours
	17

[D].

4	1	hours
	2

Answer: 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