11. 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. 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.

   
   
   

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1. View Hint View Answer Discuss in Forum

   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

   
   

   Correct Option: D

   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 .

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12. Two pipes can fill a cistern separately in 10 hours and 15 hours. They can together fill the cistern in
    

1. 1. 6 hours
      

   
   
   

   2. 7 hours
      

   
   
   

   3. 8 hours
      

   
   
   

   4. 9 hours

   
   
   

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1. View Hint View Answer Discuss in Forum

   As per the given in question , we have
   

   Part of the cistern filled by both pipes in 1 hour =	1	+	1	=	3 + 2	=	1
   	10		15		30		6

   
   

   Correct Option: A

   As per the given in question , we have
   

   Part of the cistern filled by both pipes in 1 hour =	1	+	1	=	3 + 2	=	1
   	10		15		30		6

   
   ∴ The cistern will be filled in 6 hours.

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13. Two pipes A and B can fill a tank in 36 minutes and 45 minutes respectively. Another pipe C can empty the tank in 30 minutes. First A and B are opened. After 7 minutes, C is also opened. The tank is filled up in
    

1. 1. 39 minutes
      

   
   
   

   2. 46 minutes
      

   
   
   

   3. 40 minutes
      

   
   
   

   4. 45 minutes

   
   
   

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1. View Hint View Answer Discuss in Forum

   As per the given in question , we have
   

   Part of the tank filled by pipes A and B in 1 minute =	1	+	1	=	5 + 4	=	9	=	1
   	36		45		180		180		20

   
   

   Part of the tank filled by these pipes in 7 minutes =	7
   	20

   
   

   Remaining unfilled part = 1 –	7	=	20 - 7	=	13
   	20		20		20

   
   When all three pipes are opened.
   

   =	1	-	1	=	3 - 2	=	1
   	20		30		60		60

   
   

   Correct Option: B

   As per the given in question , we have
   

   Part of the tank filled by pipes A and B in 1 minute =	1	+	1	=	5 + 4	=	9	=	1
   	36		45		180		180		20

   
   

   Part of the tank filled by these pipes in 7 minutes =	7
   	20

   
   

   Remaining unfilled part = 1 –	7	=	20 - 7	=	13
   	20		20		20

   
   When all three pipes are opened.
   

   =	1	-	1	=	3 - 2	=	1
   	20		30		60		60

   
   

   ∴ Time taken in filling	13	part	=	13	× 60 = 39 minutes
   	20			20

   
   Required time = 39 + 7 = 46 minutes

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14. One tap can fill a water tank in 40 minutes and another tap can make the filled tank empty in 60 minutes. If both the taps are open, in how many hours will the empty tank be filled ?
    

1. 1. 2 hours
      

   
   
   

   2. 2.5 hours
      

   
   
   

   3. 3 hours
      

   
   
   

   4. 3.5 hours

   
   
   

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1. View Hint View Answer Discuss in Forum

   As per the given in question , we have
   

   Part of the tank filled when both taps are opened together =	1	-	1	=	3 - 2	=	1
   	40		60		120		120

   
   

   Correct Option: A

   As per the given in question , we have
   

   Part of the tank filled when both taps are opened together =	1	-	1	=	3 - 2	=	1
   	40		60		120		120

   
   Hence, the tank will be filled in 120 minutes or 2 hours.

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15. A tank can be filled by pipe A in 2 hours and pipe B in 6 hours. At 10 A.M. pipe A was opened. At what time will the tank be filled if pipe B is opened at 11 A.M.?
    

1. 1. 12.45 A.M.
      

   
   
   

   2. 5 P.M
      

   
   
   

   3. 11.45 A.M.
      

   
   
   

   4. 12 P.M.

   
   
   

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1. View Hint View Answer Discuss in Forum

   From the given question ,
   

   Part of the tank filled in 1 hour by pipe A =	1
   	2

   
   

   Part of the tank filled by both pipes in 1 hour =	1	+	1	=	3 + 1	=	2
   	2		6		6		3

   
   So, Time taken to fill 2 /3 part = 60 minutes
   

   Correct Option: C

   From the given question ,
   

   Part of the tank filled in 1 hour by pipe A =	1
   	2

   
   

   Part of the tank filled by both pipes in 1 hour =	1	+	1	=	3 + 1	=	2
   	2		6		6		3

   
   So, Time taken to fill 2 /3 part = 60 minutes
   

   ∴ Time taken to fill	1	part	=	60 × 3	×	1	= 45 minutes
   	2			2		2

   
   ∴ The tank will be filled at 11 : 45 A.M.

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