Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A

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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:
Options
A. 6 hours
B.

6 2 hours

3
C. 7 hours
D.

7 1 hours

2

Correct Answer

7 hours

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.