31. A pipe can fill a tank in x hours and another can empty it in y hours. They can together fill it in (y > x)

1. 1. xy	hours
      y - x

   
   
   

   2. x – y hours
      

   
   
   

   3. y – x hours

   
   
   

   4. xy	hours
      x - y

   
   
   

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1. View Hint View Answer Discuss in Forum

   When both pipes are opened simultaneously,
   

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

   
   

   Correct Option: A

   When both pipes are opened simultaneously,
   

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

   
   

   ∴ Required time =	xy	hours
   	y - x

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32. Pipe A can fill an empty tank in 6 hours and pipe B in 8 hours. If both the pipes are opened and after 2 hours pipe. A is closed, how much time B will take to fill the remaining tank?
    

1. 1. 7	1	hours
      	2

   
   
   

   2. 2	2	hours
      	5

   
   
   

   3. 2	1	hours
      	3

   
   
   

   4. 3	1	hours
      	3

   
   
   

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1. View Hint View Answer Discuss in Forum

   As per the given in question , we have
   

   Part of tank filled by pipes A and B in 2 hours = 2		1	+	1
   		6		8

   
   

   Part of tank filled by pipes A and B in 2 hours = 2		4 + 3		=	7
   		24			12

   
   

   Remaining part = 1 –	7	=	5
   	12		12

   
   This part is filled by pipe B.
   

   ∴ Required time =	5	× 8
   	12

   
   

   Correct Option: D

   As per the given in question , we have
   

   Part of tank filled by pipes A and B in 2 hours = 2		1	+	1
   		6		8

   
   

   Part of tank filled by pipes A and B in 2 hours = 2		4 + 3		=	7
   		24			12

   
   

   Remaining part = 1 –	7	=	5
   	12		12

   
   This part is filled by pipe B.
   

   ∴ Required time =	5	× 8
   	12

   
   

   Required time =	10	hours	= 3	1	hours
   	3			3

   
   

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33. A cistern is normally filled in 8 hours but takes another 2 hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in :
    

1. 1. 16 hours
      

   
   
   

   2. 20 hours
      

   
   
   

   3. 25 hours
      

   
   
   

   4. 40 hours

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question , we have
   

   Part emptied by the leak in 1 hour =	1	-	1	=	5 - 4	=	1
   	8		10		40		40

   
   

   Correct Option: D

   According to question , we have
   

   Part emptied by the leak in 1 hour =	1	-	1	=	5 - 4	=	1
   	8		10		40		40

   
   ∴ The leak will empty the cistern in 40 hours.

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34. A cistern has two pipes. One can fill it with water in 8 hours and other can empty it in 5 hours. In how many hours will the cistern be emptied if both the pipes are opened together when 3/4 of the cistern is already full of water ?

1. 1. 13	1	hours
      	3

   
   
   

   2. 10 hours
      

   
   
   

   3. 6 hours

   
   
   

   4. 3	1	hours
      	3

   
   
   

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1. View Hint View Answer Discuss in Forum

   On the basis of given details in question ,
   

   Part of cistern emptied in 1 hour =	1	-	1	=	8 - 5	=	3
   	5		8		40		40

   
   

   ∵	3	part is emptied in 1 hour.
   	40

   
   

   Correct Option: B

   On the basis of given details in question ,
   

   Part of cistern emptied in 1 hour =	1	-	1	=	8 - 5	=	3
   	5		8		40		40

   
   

   ∵	3	part is emptied in 1 hour.
   	40

   
   

   ∴	3	part is emptied in	40	×	3	= 10 hours.
   	4		3		4

   
   

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35. 3/4 part of a tank is full of water.. When 30 litres of water is taken out, the tank becomes empty. The capacity of the tank is
    

1. 1. 36 litres
      

   
   
   

   2. 42 litres
      

   
   
   

   3. 40 litres
      

   
   
   

   4. 38 litres

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the capacity of the tank be q litres.
   According to the question,
   

   3q	= 30
   4

   
   ⇒ 3q = 30 × 4
   

   Correct Option: C

   Let the capacity of the tank be q litres.
   According to the question,
   

   3q	= 30
   4

   
   ⇒ 3q = 30 × 4
   

   ⇒ q =	30 × 4	= 40 litres
   	3

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