Pipes And Cistern

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

Answer: B

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).

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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

Answer: E

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).

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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

Answer: E

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

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

II. 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).

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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: C

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.

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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: C

(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.

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Questions for: Pipes And Cistern