1. 12 pumps working 6 hours a day can empty a completely filled reservoir in 15 days. How many such pumps working 9 hours a day will empty the same reservoir in 12 days?
   

1. 1. 15
      

   
   
   

   2. 9
      

   
   
   

   3. 10
      

   
   
   

   4. 12

   
   
   

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1. View Hint View Answer Discuss in Forum

   On the basis of given details in question , we have
   
   Let x be number of pumps
   ∴9 : 6 :: 12 : x = 12 : 15 :: 12 : x
   ⇒ 9 × 12 × x = 6 × 12 × 15
   

   Correct Option: C

   On the basis of given details in question , we have
   
   Let x be number of pumps
   ∴9 : 6 :: 12 : x = 12 : 15 :: 12 : x
   ⇒ 9 × 12 × x = 6 × 12 × 15
   

   ⇒ x =	6 × 12 × 15	= 10
   	9 × 12

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2. A tap can fill a cistern in 8 hours and another tap can empty it in 16 hours. If both the taps are open, the time (in hours) taken to fill the tank will be :
   

1. 1. 8
      

   
   
   

   2. 10
      

   
   
   

   3. 16
      

   
   
   

   4. 24

   
   
   

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1. View Hint View Answer Discuss in Forum

   Part of the cistern filled in 1 hour =	1
   	8

   
   

   Part of the cistern emptied in 1 hour =	1
   	16

   
   When both the taps are opened simultaneously,
   

   Part of cistern filled in 1 hour =	1	-	1	=	2 - 1	=	1
   	8		16		16		16

   
   Hence, the cistern will be filled in 16 hours.
   We can find required answer with the help of given formula :
   Here, p = 8, q = 16
   

   Required time =	pq
   	q - p

   
   

   Correct Option: C

   Part of the cistern filled in 1 hour =	1
   	8

   
   

   Part of the cistern emptied in 1 hour =	1
   	16

   
   When both the taps are opened simultaneously,
   

   Part of cistern filled in 1 hour =	1	-	1	=	2 - 1	=	1
   	8		16		16		16

   
   Hence, the cistern will be filled in 16 hours.
   We can find required answer with the help of given formula :
   Here, p = 8, q = 16
   

   Required time =	pq
   	q - p

   
   

   Required time =	8 × 16
   	16 - 8

   
   Required time = 16 hours

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3. A pipe can fill a tank in ‘x’ hours and another pipe can empty it in‘y’ (y > x) hours. If both the pipes are open, in how many hours will the tank be filled ?
   

1. 1. (x – y) hours
      

   
   
   

   2. (y – x) hours

   
   
   

   3. xy	hours
      x - y

   
   
   

   4. xy	hours
      y - x

   
   
   

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1. View Hint View Answer Discuss in Forum

   From the question ,
   

   Part of the tank filled in 1 hour =	1
   	x

   
   

   Part of the tank emptied in 1 hour =	1
   	y

   
   When both are opened , then
   

   Part of the tank filled in 1 hour =	1	-	1	=	y - x
   	x		y		xy

   
   

   Correct Option: D

   From the question ,
   

   Part of the tank filled in 1 hour =	1
   	x

   
   

   Part of the tank emptied in 1 hour =	1
   	y

   
   When both are opened , then
   

   Part of the tank filled in 1 hour =	1	-	1	=	y - x
   	x		y		xy

   
   

   ∴ Tank will be filled in	xy	hours
   	y - x

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4. Two pipes can fill a tank in 15 hours and 20 hours respectively, while the third can empty it in 30 hours. If all the pipes are opened simultaneously, the empty tank will be filled in

1. 1. 10 hours
      

   
   
   

   2. 12 hours
      

   
   
   

   3. 15 hours

   
   
   

   4. 15	1	hours
      	2

   
   
   

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1. View Hint View Answer Discuss in Forum

   On the basis of given details in question ,
   When all three pipes are opened simultaneously :
   

   Part of tank filled in 1 hour =	1	+	1	-	1
   	15		20		30

   
   

   Correct Option: B

   On the basis of given details in question ,
   When all three pipes are opened simultaneously :
   

   Part of tank filled in 1 hour =	1	+	1	-	1
   	15		20		30

   
   

   Part of tank filled in 1 hour =	4 + 3 - 2	=	5	=	1
   	60		60		12

   
   Hence, the tank will be filled in 12 hours.

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5. 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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