51. 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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52. 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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53. A tap can fill an empty tank in 12 hours and another tap can empty half the tank in 10 hours. It both the taps are opened simultaneously, how long would it take for the empty tank to be filled to half its capacity ?
    

1. 1. 30 hours
      

   
   
   

   2. 20 hours
      

   
   
   

   3. 15 hours
      

   
   
   

   4. 12 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 by pipe A in 1 hour =	1
   	12

   
   

   Part of the tank emptied by pipe B in 1 hour =	1
   	20

   
   

   Correct Option: A

   As per the given in question , we have
   

   Part of the tank filled by pipe A in 1 hour =	1
   	12

   
   

   Part of the tank emptied by pipe B in 1 hour =	1
   	20

   
   

   Part of the tank filled in 1 hour =	1	-	1	=	5 - 3	=	1
   	12		20		60		30

   
   ∴ Tank will be filled in 30 hours.

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54. Pipes P and Q can fill a tank in 10 and 12 hours respectively and C can empty it in 6 hours. If all the three are opened at 7 a.m., at what time will one-fourth of the tank be filled ?
    

1. 1. 10 a.m.
      

   
   
   

   2. 10 p.m.
      

   
   
   

   3. 11 p.m.
      

   
   
   

   4. 11 a.m.

   
   
   

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1. View Hint View Answer Discuss in Forum

   From the given question ,
   When all three pipes are opened , then
   

   Part of tank filled in 1 hour =	1	+	1	-	1
   	10		12		6

   
   

   Part of tank filled in 1 hour =	6 + 5 - 10	=	1
   	60		60

   
   ∴ The tank will be filled in 60 hours.
   

   Correct Option: B

   From the given question ,
   When all three pipes are opened , then
   

   Part of tank filled in 1 hour =	1	+	1	-	1
   	10		12		6

   
   

   Part of tank filled in 1 hour =	6 + 5 - 10	=	1
   	60		60

   
   ∴ The tank will be filled in 60 hours.
   

   ∴ One fourth of the tank will be filled in 15 hours =		1	× 60		i.e the tank will be filled at 10 p.m.
   		4

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55. If 3/5 th of a cistern is filled in 1 minute, the time needed to fill the rest is
    

1. 1. 40 sec
      

   
   
   

   2. 30 sec
      

   
   
   

   3. 36 sec
      

   
   
   

   4. 24 sec

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question ,
   

   Time taken to fill the	3	of the cistern = 60 seconds
   	5

   
   

   ∴ Time taken in filling	2	part =	60 × 5	×	2
   	5		3		5

   Correct Option: A

   According to question ,
   

   Time taken to fill the	3	of the cistern = 60 seconds
   	5

   
   

   ∴ Time taken in filling	2	part =	60 × 5	×	2	= 40 second
   	5		3		5

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