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21. Two pipes A and B can fill a tank in 12 minutes and 16 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 9 minutes?
  A.  4 minutes
  B.  6 minutes
  C.  7 minutes
  D.  3 minutes
     
   
View Answer

Shortcut:
Two pipes X and Y can fill a tank in 'a' minutes and 'b' minutes respectively. If both the pipes are opened simultaneously, then the time after which pipe Y should be closed, so that the tank is full in 't' minutes is b x
(
1 −
t / a
)
minutes.
Here, a = 12, b = 16, t = 9
Using these values in the shortcut, we get:
Required time = 16 x
(
1 −
9 / 12
)

= 16 x
(
1 −
3 / 4
)

= 16 x
4 −3 / 4

= 16 x
1 / 4
= 4 x 1 = 4
Hence, the required time is 4 minutes.

22. Two pipes A and B can fill a cistrn in 40 minutes and 50 minutes respectively. Both are opened together, but at the end of 10 minutes, B is turned off. How much longer will the cistern take to fill?
  A.  35 minutes
  B.  30 minutes
  C.  32 minutes
  D.  27 minutes
     
   
View Answer

Shortcut:
Two pipes X and Y can fill a tank in 'a' minutes and 'b' minutes respectively. If both the pipes are opened simultaneously, then the time after which pipe Y should be closed, so that the tank is full in 't' minutes is b x
(
1 −
t / a
)
minutes.
Here, a = 40, b = 50, t = ?, Required Time = 10
Using these values in the shortcut, we get:
Required time = 50 x
(
1 −
t / 40
)

10 = 50 x
40 − t / 40

10 x 40 = 50(40 − t)
8 = 40 − t
t = 40 − 8
t = 32
Hence, the cistern will take 32 minutes to fill.

23. Two pipes A and B would fill a cistern in 12 hours and 16 hours respectively. If both pipes are opened together, find when the first pipe must be turned off so that the cistern may be just filled in 8 hours.
  A.  3 hours
  B.  6 hours
  C.  5 hours
  D.  9 hours
     
   
View Answer

Shortcut:
Two pipes X and Y can fill a tank in 'a' hours and 'b' hours respectively. If both the pipes are opened simultaneously, then the time after which pipe X should be closed, so that the tank is full in 't' hours is a x
(
1 −
t / b
)
hours.
Here, a = 12, b = 16, t = 8
Using these values in the shortcut, we get:
Required time = 12 x
(
1 −
8 / 16
)

= 12 x
(
1 −
1 / 2
)

= 12 x
2 − 1 / 2

= 12 x
1 / 2
= 6
Hence, after 6 hours, pipe must be turned off.

24. Two pipes, A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
  A.  8
1 / 4
minutes
  B.  5
1 / 4
minutes
  C.  8
7 / 2
minutes
  D.  7
3 / 4
minutes
     
   
View Answer

Shortcut:
Two pipes X and Y can fill a tank in 'a' hours and 'b' hours respectively. If both the pipes are opened simultaneously, then the time after which pipe X should be closed, so that the tank is full in 't' hours is a x
(
1 −
t / b
)
hours.
Here, a = 12, b = 15, t = ?, Required time = 3
Using these values in the shortcut, we get:
Required time = 12 x
(
1 −
t / 15
)

3 = 12 x
15 − t / 15

3 x 15 = 12(15 − t)
15 = 4(15 − t)
15 = 60 − 4t
4t = 60 − 15
4t = 45
t =
45 / 4
= 11
1 / 4

∴ Required answer =
45 / 4
− 3 =
45 − 12 / 4
=
33 / 4
= 8
1 / 4
minutes
Hence, the cistern will take 8
1 / 4
minutes to fill.

25. Two pipes A and B can fill a cistern in 5 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
  A.  8 minutes
  B.  3 minutes
  C.  6 minutes
  D.  10 minutes
     
   
View Answer

Shortcut:
Two pipes X and Y can fill a tank in 'a' hours and 'b' hours respectively. If both the pipes are opened simultaneously, then the time after which pipe X should be closed, so that the tank is full in 't' hours is a x
(
1 −
t / b
)
hours.
Here, a = 5, b = 15, t = ?, Required time = 3
Using these values in the shortcut, we get:
Required time = 5 x
(
1 −
t / 15
)

3 = 5 x
15 − t / 15

3 x 15 = 5(15 − t)
3 x 3 = 15 − t
9 = 15 − t
t = 15 − 9
t = 6
∴ Required answer = 6 − 3 = 3
Hence, the cistern will take 3 minutes to get filled.

26. If two pipes function simultaneously, the reservior is filled in 6 hours. One pipe fill the reservoir 5 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
  A.  10 hours
  B.  7 hours
  C.  5 hours
  D.  11 hours
     
   
View Answer

Shortcut:
If two pipes X and Y function simultaneously, the tank is filled in 'a' hours and pipe X fills the tank 'b' hour faster than the other, then the time taken by the faster pipe X to fill the tank is
√[b2 + 4a2] − (b − 2a) / 2
hours.
Here, a = 6, b = 5
Using these values in the shortcut, we get:
Required time =
√[(5)2 + 4 x (6)2] − (5 − 2 x 6) / 2

=
√[25 + 4 x 36] − (5 − 12) / 2

=
√[25 + 144] − (− 7) / 2

=
√[169] + 7) / 2

=
13 + 7 / 2
=
20 / 2
= 10
Hence, the faster pipe will take 10 hours to fill the reservoir.

27. Three pipes A, B and C can fill a cistern in 3 hours. After working together for 1 hours, C is closed and A and B fill the cistern in 4 hours. Then find the time in which the cistern can be filled by pipe C
  A.  3 hours
  B.  5 hours
  C.  4 hours
  D.  6 hours
     
   
View Answer

Shortcut:
Three pipes X, Y and Z can fill a tank in 'a' hours. If after working together for 't' hours, Z is closed and X and Y fill the tank in 'b' hours, then the time in which the tank cn be filled by the pipe Z is
a x b / b − a + t
hours.
Here, a = 3, b = 4, t = 1
Using these values in the shortcut, we get:
Required time =
3 x 4 / 4 − 3 + 1

=
3 x 4 / 1 + 1
=
3 x 4 / 2
= 3 x 2 = 6
Hence, pipe C will take 6 hours to fill the cistern.

28. If two pipes function simultaneously the reservoir is filled in 12 minutes. One pipe fills the reservoir 10 minutes faster than the other. How many hours does the fster pipe take to fill the reservoir?
  A.  11 minutes
  B.  25 minutes
  C.  20 minutes
  D.  12 minutes
     
   
View Answer

Shortcut:
If two pipes X and Y function simultaneously, the tank is filled in 'a' hours and pipe X fills the tank 'b' hour faster than the other, then the time taken by the faster pipe X to fill the tank is
√[b2 + 4a2] − (b − 2a) / 2
hours.
Here, a = 12, b = 10
Using these values in the shortcut, we get:
Required time =
√[(10)2 + 4 x (12)2] − (10 − 2 x 12) / 2

=
√[100 + 4 x 144] − (10 − 24) / 2

=
√[100 + 576] − (− 14) / 2

=
√[676] + 14) / 2

=
26 + 14 / 2
=
40 / 2
= 20
Hence, the faster pipe will take 20 hours to fill the reservoir.

29. Pipe A can fill a tank in 24 minutes and another pipe in 30 minutes, but a third pipe can empty it in 12 minutes. The first two pipes are kept open for 10 minutes in the beginning and then the third pipe is also opened. In what time is the cistern emptied?
  A.  80 minutes
  B.  90 minutes
  C.  100 minutes
  D.  78 minutes
     
   
View Answer

Shortcut:
A pipe can fill a tank in 'a' unit of time and another pipe in 'b' unit of time, but a third pipe can empty it in 'c' unit of time. If the first two pipes are kept open for 't' unit of time in the beginning and then the third pipe is also opened, the time in which the cistern is emptied is
c x t / ab/(a + b) − c
unit of time.
Here, a = 24, b = 30, c = 12, t = 10
Using these values in the shortcut, we get:
Required time =
12 x 10 / 24 x 30/(24 + 30) − 12

=
12 x 10 / 24 x 30/54 − 12

=
12 x 10 / 40/3 − 12

=
12 x 10 / (40 − 36)/3

=
12 x 10 / 4/3

=
12 x 10 x 3 / 4
= 3 x 10 x 3 = 90
Hence, the cistern will get emtpy in 90 minutes.

30. A, B and C are three pipes connected to a tank. A and B together fill the tank in 12 hours. B and C together ill the tank in 20 hours. A and C together fill the tank in 15 hours. In how much time will A,B anc C fill the tank separately?
  A.  A in 20 hours; B in 30 hours; C in 60 hours
  B.  A in 25 hours; B in 32 hours; C in 55 hours
  C.  A in 15 hours; B in 35 hours; C in 45 hours
  D.  A in 22 hours; B in 25 hours; C in 50 hours
     
   
View Answer

Shortcut:
X, Y and Z are three pipes connected to a tank. X and Y together fill the tank in 'a' hours. Y and Z together fill the tank in 'b' hours. X and Z together fill the tank in 'c' hours. (i) Time taken by X to fill the tank =
2abc / ab + bc − ac
hours.
(ii) Time taken by Y to fill the tank =
2abc / bc + ac − ab
hours.
(iii) Time taken by Z to fill the tank =
2abc / ac + ab − bc
hours.
Here, a = 12, b = 20, c = 15
Using these values in the shortcut, we get:
Time taken by A to fill the tank =
2 x 12 x 20 x 15 / 12 x 20 + 20 x 15 − 12 x 15

=
2 x 12 x 20 x 15 / 240 + 300 − 180

=
2 x 12 x 20 x 15 / 540 − 180

=
2 x 12 x 20 x 15 / 360
= 2 x 2 x 5 = 20
Hence, pipe A will fill the tank in 20 hours.
Time taken by B to fill the tank =
2 x 12 x 20 x 15 / 20 x 15 + 12 x 15 − 12 x 20

=
2 x 12 x 20 x 15 / 300 + 180 − 240

=
2 x 12 x 20 x 15 / 480 − 240

=
2 x 12 x 20 x 15 / 240
= 2 x 15 = 30
Hence, pipe B will fill the tank in 30 hours.
Time taken by Z to fill the tank =
2 x 12 x 20 x 15 / 12 x 15 + 12 x 20 − 20 x 15

=
2 x 12 x 20 x 15 / 180 + 240 − 300

=
2 x 12 x 20 x 15 / 420 − 300

=
2 x 12 x 20 x 15 / 120
= 2 x 2 x 15 = 60
Hence, pipe C will fill the tank in 60 hours.

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