Aptitude

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.