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1. A pipe can fill a tank in 10 hours. Find the part of tank filled in one hour.
  A.  
2 / 3
  B.  
3 / 8
  C.  
1 / 10
  D.  
1 / 5
     
   
View Answer

Shortcut:
If a pipe can fill a tank in 'y' hours, then the part filled in 1 hour is
1 / y
.
Here, y = 10
Using these values in the shortcut, we get:
The part filled in 1 hour =
1 / 10

2. A pipe can empty a tank in 12 hours. Find the part of the tank emptied in one hour.
  A.  
1 / 12
  B.  
1 / 8
  C.  
1 / 11
  D.  
1 / 15
     
   
View Answer

Shortcut:
If a pipe can empty a tank in 'y' hours, then the part emptied in 1 hour is
1 / y
.
Here, y = 12
Using these values in the shortcut, we get:
The part emptied in 1 hour =
1 / 12

3. A pipe can empty a cistern in 27 hours. Find the time in which
2 / 3
part of the cistern will be emptied.
  A.  9 hours
  B.  16 hours
  C.  11 hours
  D.  18 hours
     
   
View Answer

Shortcut:
If a pipe can empty a tank in 'y' hours, then the part emptied in 1 hour is
1 / y
.
Here, y = 27
Using these values in the shortcut, we get:
The part emptied in 1 hour =
1 / 27

1 / 27
part is emptied in 1 hour
or, 1 part is emptied in 27 hours
Then,
2 / 3
part will be emptied in
2 / 3
x 27 = 2 x 9 = 18
Hence,
2 / 3
part will be emptied in 18 hours.

4. A pipe can fill a tank in 10 hours and another pipe can empty it in 12 hours. If both the pipes are opened, find the time in which tank is filled.
  A.  55 hours
  B.  60 hours
  C.  70 hours
  D.  None of the above
     
   
View Answer

Shortcut:
If a pipe can fill a tank in y hours and another pipe can empty the full tank in z hours, then the net part filled in 1 hour, when both the pipes are opened is
1 / y
−
1 / z
. Therefore, Time taken to fill the tank, when both the pipes are opened =
yz / z − y

Here, y = 10, z = 12
Using these values in the shortcut, we get:
Required time =
10 x 12 / 12 − 10
=
10 x 12 / 2
= 10 x 6 = 60
Hence, the tank will be filled in 60 hours.

5. A water tank is
2 / 5
th full. Pipe A can fill the tank in 10 minutes and the pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?.
  A.  8 minutes
  B.  10 minutes
  C.  5 minutes
  D.  6 minutes
     
   
View Answer

Shortcut:
If a pipe can fill a tank in y hours and another pipe can empty the full tank in z hours, then the net part filled in 1 hour, when both the pipes are opened is
1 / y
−
1 / z
. Therefore, Time taken to fill the tank, when both the pipes are opened =
yz / z − y

Here, y = 10, z = 6
Using these values in the shortcut, we get:
Required time =
10 x 6 / 6 − 10
=
10 x 6 / − 4
= − 5 x 3 = − 15
−ve sign indicates that the tank will get empty.
∴ the full tank will get emtpy in 15 minutes.
So,
2 / 5
th full tank will get empty in
2 / 5
x 15 = 2 x 3 = 6 minutes.

6. Pipe A fills the cistern in half an hour and pipe B in 40 minutes, but owing to a crack in the bottom of the cistern it is found that pipe A now takes 40 minutes to fill the cistern. How long will B take now to fill it and how long will the crack take to empty it?
  A.  B fills in an hour and the leak empties in 2 hours
  B.  B fills in 3 hours and the leak empties in half an hour
  C.  B fills in 2 hours and the leak empties in 40 minutes
  D.  B fills in an hour and the leak empties in 50 minutes
     
   
View Answer

Shortcut:
If a pipe can fill a tank in y hours and another pipe can empty the full tank in z hours, then the net part filled in 1 hour, when both the pipes are opened is
1 / y
−
1 / z
. Therefore, Time taken to fill the tank, when both the pipes are opened =
yz / z − y

Here, y = 30, z = ?, Time = 40
Using these values in the shortcut, we get:
Required time =
30 x z / z − 30

40 =
30 x z / z − 30

40 x (z − 30) = 30z
40z − 1200 = 30z
40z − 30z = 1200
10z = 1200
z =
1200 / 10
= 120 minutes or 2 hours
Now, from the question, applying the rule we have, time taken by B to fill the tank when crack in the bottom develops =
120 x 40 / 120 − 40
= 60 minutes = 1 hour

7. A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full, in what time will the leak empty it?
  A.  80 hours
  B.  90 hours
  C.  100 hours
  D.  85 hours
     
   
View Answer

Shortcut:
If a pipe can fill a tank in y hours and another pipe can empty the full tank in z hours, then the net part filled in 1 hour, when both the pipes are opened is
1 / y
−
1 / z
. Therefore, Time taken to fill the tank, when both the pipes are opened =
yz / z − y

Here, y = 9, z = ?, Time = 9 + 1 = 10
Using these values in the shortcut, we get:
Required time =
30 x z / z − 30

10 =
9 x z / z − 9

10 x (z − 9) = 9z
10z − 90 = 9z
10z − 9z = 90
z = 90
Hence, the leak will empty the full tank in 90 hours.

8. A tap can fill a tank in 25 minutes and another can empty it in 50 minutes. If the tank is already half full and both the taps are opened together, the
  A.  Tank is emptied in 30 minutes
  B.  Tank is filled up in 20 minutes
  C.  Tank is filled up in 25 minutes
  D.  Tank is emptied in 24 minutes
     
   
View Answer

Shortcut:
If a pipe can fill a tank in y hours and another pipe can empty the full tank in z hours, then the net part filled in 1 hour, when both the pipes are opened is
1 / y
−
1 / z
. Therefore, Time taken to fill the tank, when both the pipes are opened =
yz / z − y

Here, y = 25, z = 50
Using these values in the shortcut, we get:
Required time =
1 / 2
x
25 x 50 / 50 − 25

=
1 / 2
x
25 x 50 / 25

=
1 / 2
x 50 = 25
Hence, the tank will get filled in 25 minutes.

9. A pipe can fill
1 / 4
of cistern in 16 minutes. In how many minutes, it can fill
3 / 4
of the cistern?
  A.  48 minutes
  B.  50 minutes
  C.  45 minutes
  D.  None of the above
     
   
View Answer

Shortcut:
If a tap can fill a m1 part of the cistern in t1 minutes and m2 part in t2 minutes, then following expression is obtained
t1 / m1
=
t2 / m2
.
Here, t1 = 16, t2 = ?, m1 =
1 / 4
, m2 =
3 / 4

Using these values in the shortcut, we get:
16 / 1/4
=
t2 / 3/4

t2 =
16 x 3/4 / 1/4

t2 =
16 x 3 x 4 / 4
= 16 x 3 = 48
Hence, the tank will get filled in 48 minutes.

10. A pipe can empty
2 / 3
of cistern in 8 minutes. In 9 minutes what part of cistern will be emptied?
  A.  
3 / 2
part of the cistern will be emptied
  B.  
2 / 3
part of the cistern will be emptied
  C.  
4 / 3
part of the cistern will be emptied
  D.  
3 / 4
part of the cistern will be emptied
     
   
View Answer

Shortcut:
If a tap can empty m1 part of the cistern in t1 minutes and m2 part in t2 minutes, then following expression is obtained
t1 / m1
=
t2 / m2
.
Here, t1 = 8, t2 = 9, m1 =
2 / 3
, m2 = ?
Using these values in the shortcut, we get:
8 / 2/3
=
9 / m2

m2 =
9 x 2/3 / 8

m2 =
3 x 2 / 8
=
3 / 4

Hence,
3 / 4
part of cistern will get emptied.

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