Two pipes P and Q can fill a tank in 6 hours and 9 hours

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Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed. The total time taken to fill the tank (in hours) is _____.

1. 13.50
2. 16.50
3. 14.50
4. 15.50

Correct Option: C

Here,

In 1 hr, part of tank filled by P alone is =	1
	6

In 1 hr, part of tank filled by Q alone is =	1
	9

In 1 hr, part of tank emptied by R is =	1
	12

Initially, P and R opened for 4 hr,

So part of tank filled = 4		1	-	1			= (4 / 12) = (1 / 3)
		6		12

After 4 hr, P is closed and for 6 more hr Q and R are opened.

So part of tank filled = 6		1	-	1			= (1 / 6)
		9		12

So, total tank filled in 10 hr =		1	+	1	=	2 + 4	=	1
		6		3		12		2

So, remaining 1/2 part of the tank is filled by Q alone
Now, Q will take 9/2 = 4.5 hr to fill remaining half of the tank.
Hence, total time taken = 4 + 6 + 4.5 = 14.5 hr