Two pipes A and B can separately fill a cistern in 60 minutes

Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time the third pipe alone can empty the cistern?

Let the third pipe empty the cistern in t minutes. when all three pipes are opened simultaneously

Part of cistern filled in 1 minute =	1	+	1	-	1
	60		75		t

According to the question,

∴	1	+	1	-	1	=	1
	60		75		t		50

⇒	1	=	1	+	1	-	1
	t		60		75		50

=	5 + 4 - 6	=	3	⇒	1	=	3
	300		300		t		300

∴ t =	300	= 100 minutes.
	3