Two pipes A and B can fill a cistern in 37½ 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:

5 min.
9 min.
10 min.
15 min.

Correct Answer: 9 min.

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.

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