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1.
Two pipes A and B can fill a cistern in 10 minutes and 15 minutes respectively, and a tap C can empty the full cistern in 20 minutes. All the three were opened for 1 minute and then the emptying tap was closed?
  • A.
    		 5 3  
    10  
  • C.
    8
  • B.
    		 7 4  
    10  
  • D.
    5
  • Answer & Explanation
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Answer : [A]
Explanation :
Part of the cistern filled by all the 3 pipes in 1 minute =
1
10
+
1
15
-
1
20
=
6 + 4 - 3
60
=
7
60
 
Remaining part =
53
60
 ( This has to be filled by pipes A and B)
A and B can fill
1
10
+
1
15
+
1
6
  part of the cistern in 1 minute  
 
 
53
60
  part can be filled in =
53
60
 x 6 =
53
10
 = 5
3
10
 min.  
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2.
Two pipes A and B can fill a tank in 12 and 16 minutes respectively. Both pipes are opened together, but 4 minutes before the tank is full, one pipe A is closed. How much time will they take to fill the tank?
  • A.
    9 minutes
  • B.
    		 9 1  minutes  
    7  
  • B.
    		 9 2  minutes  
    7  
  • B.
    		 9 3  minutes  
    7  
  • Answer & Explanation
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Answer : [B]
Explanation :
Let the cistern be filled in x minutes
 
  Pipe B is opened for x minutes and pipe A is opened for x – 4 minutes.  
Let the total work = 1
 
  A’s amount of work + B’s work = 1  
A’s open time
Time taken by A alone
+
B’s open time
Time taken by B alone
 = 1
x - 4
12
+
x
16
 = 1
 
 
4(x - 4) + 3x
48
 = 1
7x = 48 + 16
 
  7x = 64
 
  x =
64
7
 = 9
1
7
 minutes  
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3.
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
  • A.
    8
  • C.
    16
  • B.
    10
  • D.
    24
  • Answer & Explanation
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Answer : [C]
Explanation :
Part of the cistern filled in 1 hr. =
1
8
 
Part of the cistern emptied in 1 hr. =
1
16
 
When both the taps are opened simultaneously. Part of cistern filled in 1 hour =
1
8
-
1
16
=
2-1
16
=
1
16
 
 
  Cistern will be filled in 16 hours.    
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4.
Two pipes can fill a cistern in 6 minutes and 7 minutes respectively. Both the pipes are opened alternatively for 1 minute each. In what time will they fill the cistern?
  • A.
    5 minutes
  • B.
    		 6 3  minutes  
    7  
  • B.
    		 5 2  minutes  
    3  
  • B.
    		 1 1  minutes  
    4  
  • Answer & Explanation
  • Report
Answer : [B]
Explanation :
Part of the cistern filled by first pipe in 1 minute =
1
6
 
Part of the cistern filled by second pipe in 2 minutes =
1
7
 
Part of cistern filled in first 2 minutes =
1
6
+
1
7
=
13
42
 
Part of cistern filled in 6 minutes =
3 x 13
42
=
39
42
 
Remaining part = 1 -
39
42
=
3
42
=
1
14
 
Now it is turn for pipe one. Time taken to fill
1
14
part =
6
14
=
3
7
 
 
  Total time = 6 +
3
7
 = 6
3
7
 minutes.  
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5.
Two pipes A and B can fill a tank is 12 minutes and 15 minutes respectively. If both the taps are opened simultaneously, and the tap A is closed after 3 minutes, then how much more time will it take to fill the tank by tap B?
  • A.
    7 min 15 sec
  • C.
    8 min 5 sec
  • B.
    7 min 45 sec
  • D.
    8 min 15 sec
  • Answer & Explanation
  • Report
Answer : [D]
Explanation :
 
Part filled in 3 min. = 3  
1
12
+
1
15
  =   3 x
9
60
  =
9
20
 
 
Remaining part =   1 -
9
20
  =
11
20
   
 
Part filled by B in 1 min. =
1
15
       
 
1
15
:
11
20
 :: 1 : x    or     x =  
11
20
 x 1 x 15    = 8
1
4
 min. = 8 min. 15 sec  
 
    Remaining part is filled by B in 8 min. 15 sec.            
 
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