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
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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
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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
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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
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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
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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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