Three pipes P, Q and R can separately fill a cistern in

Three pipes P, Q and R can separately fill a cistern in 4,8 and 12 hours respectively. Another pipe S can empty the completely filled cistern in10 hours. Which of the following arrangements will fill the empty cistern in less time than others ?

1. Q alone is open.
2. P and S are open.
3. P, R and S are open.
4. P, Q and S are open.

According to question ,
When pipes P and S are open , then

Part of the cistern filled in 1 hour =	1	-	1	=	5 - 2	=	3
	4		10		20		20

Hence, the cistern will be filled in 20 / 3 hours ≈ 6.6 hours
When pipes P, R and S are open ,

Part of the cistern filled in 1 hour =	1	+	1	-	1
	4		12		10

Part of the cistern filled in 1 hour =	15 + 5 - 6	=	14	=	7
	60		60		30

Hence, the cistern will be filled in	30	hours ≈ 4.3 hours
	7

When pipes P, Q and S are open , then

Part of the cistern filled in I hour =	1	+	1	-	1
	4		8		10

Part of the cistern filled in I hour =	10 + 5 - 4	=	11
	40		40

Hence, the cistern will be filled in	40	hours ≈ 3.6 hours
	11

∴ Cistern can be filled faster when P, Q & S are open .