6. 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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7. A cistern can be filled with water by a pipe in 5 hours and it can be emptied by a second pipe in 4 hours. If both the pipes are opened when the cistern is full, the time in which it will be emptied is :
   

1. 1. 9 hours
      

   
   
   

   2. 18 hours
      

   
   
   

   3. 20 hours

   
   
   

   4. 20	1	hours
      	2

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to the question ,
   

   Cistern filled in 1 hour =	1	part
   	5

   
   

   Cistern emptied in 1 hour =	1	part
   	4

   
   When the both pipes are opened, simultaneously ;
   

   Cistern emptied in 1 hour =	1	-	1	=	5 - 4	=	1	part
   	4		5		20		20

   
   ∴ The time in which it will be emptied = 20 hours.
   Using the given formula :
   Here, p = 5, q = 4
   

   Required time =		pq		hrs
   		(p - q)

   
   

   Correct Option: C

   According to the question ,
   

   Cistern filled in 1 hour =	1	part
   	5

   
   

   Cistern emptied in 1 hour =	1	part
   	4

   
   When the both pipes are opened, simultaneously ;
   

   Cistern emptied in 1 hour =	1	-	1	=	5 - 4	=	1	part
   	4		5		20		20

   
   ∴ The time in which it will be emptied = 20 hours.
   Using the given formula :
   Here, p = 5, q = 4
   

   Required time =		pq		hrs
   		(p - q)

   
   

   Required time =	5 × 4	= 20 hrs.
   	5 - 4

   
   

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8. Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. If both pipes are opened together, the time taken to fill the tank is :
   

1. 1. 50 minutes
      

   
   
   

   2. 12 minutes
      

   
   
   

   3. 25 minutes
      

   
   
   

   4. 15 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 both pipes in one minute =	1	+	1
   	20		30

   
       1

   Required time =
   	1	+	1
   	20		30

   
   

   Required time =	20 × 30	= 12 minutes
   	50

   
   We can find required answer with the help of given formula :
   Here, p = 20, q = 30
   

   Required time =		pq		minutes.
   		p + q

   
   

   Correct Option: B

   As per the given in question , we have
   

   Part of the tank filled by both pipes in one minute =	1	+	1
   	20		30

   
       1

   Required time =
   	1	+	1
   	20		30

   
   

   Required time =	20 × 30	= 12 minutes
   	50

   
   We can find required answer with the help of given formula :
   Here, p = 20, q = 30
   

   Required time =		pq		minutes.
   		p + q

   
   

   Required time =		20 × 30		minutes.
   		20 + 30

   
   Required time = 12 minutes.

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9. A tap can empty a tank in one hour. A second tap can empty it in 30 minutes. If both the taps operate simultaneously, how much time is needed to empty the tank?
   

1. 1. 20 minutes
      

   
   
   

   2. 30 minutes
      

   
   
   

   3. 40 minutes
      

   
   
   

   4. 45 minutes

   
   
   

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1. View Hint View Answer Discuss in Forum

   We know that , 1 hour = 60 minutes.
   Rate of emptying the tank by the two taps are 1 /60 and 1 / 30 of the tank per minute respectively.
   When both operate simultaneously ,
   

   Rate of emptying the tank =	1	+	1	=	1 + 2	=	3	=	3	of the tank per minute.
   	60		30		60		60		20

   
   ∴ Time taken by the two taps together to empty the tank = 20 minutes
   Second method to solve this question :
   Here, p = 60, q = 30
   

   Required time =		pq		minutes
   		(p + q)

   
   

   Correct Option: A

   We know that , 1 hour = 60 minutes.
   Rate of emptying the tank by the two taps are 1 /60 and 1 / 30 of the tank per minute respectively.
   When both operate simultaneously ,
   

   Rate of emptying the tank =	1	+	1	=	1 + 2	=	3	=	3	of the tank per minute.
   	60		30		60		60		20

   
   ∴ Time taken by the two taps together to empty the tank = 20 minutes
   Second method to solve this question :
   Here, p = 60, q = 30
   

   Required time =		pq		minutes
   		(p + q)

   
   

   Required time =		60 × 30		minutes
   		60 + 30

   
   Required time = 20 minutes.

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10. Three taps A,B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes.How long will the tap C alone take to fill it ?
    

1. 1. 16 minutes
      

   
   
   

   2. 24 minutes
      

   
   
   

   3. 32 minutes
      

   
   
   

   4. 40 minutes

   
   
   

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1. View Hint View Answer Discuss in Forum

   On the basis of given details in question ,
   

   Part of the cistern filled by taps A, B and C in 1 minute =	1
   	10

   
   

   Part of the cistern filled by taps A and B in 1 minute =	1	+	1	=	4 + 3	=	7
   	30		40		120		120

   
   

   Correct Option: B

   On the basis of given details in question ,
   

   Part of the cistern filled by taps A, B and C in 1 minute =	1
   	10

   
   

   Part of the cistern filled by taps A and B in 1 minute =	1	+	1	=	4 + 3	=	7
   	30		40		120		120

   
   

   ∴ Part of the cistern filled by tap C in 1 minute =	1	-	7	=	12 - 7	=	5	=	1
   	10		120		120		120		24

   
   ∴ Tap C will fill the cistern in 24 minutes.

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