16. Two pipes, P and Q, together can fill a cistern in 20 minutes and P alone can in 30 minutes. Then Q alone can fill the cistern in
    

1. 1. 62 minutes
      

   
   
   

   2. 60 minutes
      

   
   
   

   3. 61 minutes
      

   
   
   

   4. 51 minutes

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question ,
   

   Part of the cistern filled by pipe Q in 1 minute =	1	-	1	=	3 - 2	=	1
   	20		30		60		60

   
   

   Correct Option: B

   According to question ,
   

   Part of the cistern filled by pipe Q in 1 minute =	1	-	1	=	3 - 2	=	1
   	20		30		60		60

   
   ∴ Required time = 60 minutes

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17. Two pipes A and B can fill a cistern in 3 hours and 5 hours respectively. Pipe C can empty in 2 hours. If all the three pipes are open, in how many hours the cistern will be full?
    

1. 1. can’t be filled
      

   
   
   

   2. 10 hours
      

   
   
   

   3. 15 hours
      

   
   
   

   4. 30 hours

   
   
   

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1. View Hint View Answer Discuss in Forum

   As per the given in question , we have
   

   Part of cistern filled by two pipes in an hour =	1	+	1
   	3		5

   
   

   Part of the tank emptied in 1 hour by pipe C =	1
   	2

   
   

   Correct Option: D

   As per the given in question , we have
   

   Part of cistern filled by two pipes in an hour =	1	+	1
   	3		5

   
   

   Part of the tank emptied in 1 hour by pipe C =	1
   	2

   
   

   Part of cistern filled by three pipes in an hour =	1	+	1	-	1	=	10 + 6 - 15	=	1
   	3		5		2		30		30

   
   Hence, the cistern will be filled in 30 hours.

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18. Three taps A, B, C can fill an overhead tank in 4, 6 and 12 hours respectively. How long would the three taps take to fill the tank if all of them are opened together ?
    

1. 1. 2 hrs.
      

   
   
   

   2. 4 hrs.
      

   
   
   

   3. 3 hrs.
      

   
   
   

   4. 5 hrs.

   
   
   

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1. View Hint View Answer Discuss in Forum

   On the basis of given details in question ,
   

   Part of the tank filled by all three taps in an hour =	1	+	1	+	1	=	6 + 4 + 2	=	1
   	4		6		12		24		2

   
   

   Correct Option: A

   On the basis of given details in question ,
   

   Part of the tank filled by all three taps in an hour =	1	+	1	+	1	=	6 + 4 + 2	=	1
   	4		6		12		24		2

   
   ∴ Hence, the tank will be filled in 2 hours.

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19. If two pipes function simultaneously, a tank is filled in 12 hours. One pipe fills the tank 10 hours faster than the other. How many hours does the faster pipe alone take to fill the tank?
    

1. 1. 20 hrs
      

   
   
   

   2. 18 hrs
      

   
   
   

   3. 15 hrs
      

   
   
   

   4. 12 hrs

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the slower pipe fills the tank in t hours, then
   According to question ,
   

   ∴	1	+	1	=	1
   	t		t - 10		12

   
   

   ⇒	t - 10 + t	=	1
   	t(t - 10)		12

   
   ⇒ t² – 10t = 24t – 120
   ⇒ t² – 34t + 120 = 0
   ⇒ t² – 30t – 4t + 120 = 0
   

   Correct Option: A

   Let the slower pipe fills the tank in t hours, then
   According to question ,
   

   ∴	1	+	1	=	1
   	t		t - 10		12

   
   

   ⇒	t - 10 + t	=	1
   	t(t - 10)		12

   
   ⇒ t² – 10t = 24t – 120
   ⇒ t² – 34t + 120 = 0
   ⇒ t² – 30t – 4t + 120 = 0
   ⇒ t (t – 30) – 4 (t – 30) = 0
   ⇒ (t – 4) (t – 30) = 0
   ∴ t = 30 because t ≠ 4
   ∴ Required time = 30 – 10 = 20 hours

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20. Two pipes X and Y can fill a cistern in 24 minutes and 32 minutes respectively. If both the pipes are opened together, then after how much time (in minutes) should Y be closed so that the tank is full in 18 minutes ?
    

1. 1. 10
      

   
   
   

   2. 8
      

   
   
   

   3. 6
      

   
   
   

   4. 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   If pipe Y be closed after t minutes, then
   According to question ,
   

   18	+	t	= 1
   24		32

   
   

   ⇒	t	= 1 -	18	= 1 -	3	=	1
   	32		24		4		4

   
   

   ⇒ t =	32	= 8 minutes
   	4

   
   We can find required answer with the help of given formula :
   Here , p = 24, q = 32, t = 18
   

   Required time =		q		1 -	t			minutes
   					p

   
   

   Correct Option: B

   If pipe Y be closed after t minutes, then
   According to question ,
   

   18	+	t	= 1
   24		32

   
   

   ⇒	t	= 1 -	18	= 1 -	3	=	1
   	32		24		4		4

   
   

   ⇒ t =	32	= 8 minutes
   	4

   
   We can find required answer with the help of given formula :
   Here , p = 24, q = 32, t = 18
   

   Required time =		q		1 -	t			minutes
   					p

   
   

   Required time =		32		1 -	18			minutes
   					24

   
   

   Required time =		32		1 -	3
   					4

   
   

   Required time = 32 ×	1	= 8 minutes
   	4

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