Pipes and Cistern- General Questions

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.

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 2/3 hours
C.	7 hours
D.	7 1/2 hours

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.

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

Answer: 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.

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

Answer: 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.

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.

Answer: 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.

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.

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

Answer: 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

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]

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