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11. A pipe can empty a tank in 20 hours and another pipe can empty it in 10 hours. If both the pipes are opened simultaneously, find the time in which a full tank is emptied.
  A.  3
3 / 5
hours
  B.  4
3 / 4
hours
  C.  6
2 / 3
hours
  D.  3
4 / 3
hours
     
   
View Answer

Shortcut:
A tap X can empty a cistern in a hours and the other tap Y can empty it in b hours. If both emptying taps are opened together, then the time taken to empty the full cistern is
ab / a + b

Here, a = 20, b = 10
Using these values in the shortcut, we get:
Required time =
20 x 10 / 20 + 10
=
200 / 30
=
20 / 3
= 6
2 / 3

Hence, the full tank will get emtpy in 6
2 / 3
hours.

12. A pipe can empty a tank in 10 hours and another pipe can empty it in 15 hours. If both the pipes are opened simultaneoously, find the time in which a full tank is emptied.
  A.  5 hours
  B.  3 hours
  C.  4 hours
  D.  6 hours
     
   
View Answer

Shortcut:
A tap X can empty a cistern in a hours and the other tap Y can empty it in b hours. If both emptying taps are opened together, then the time taken to empty the full cistern is
ab / a + b

Here, a = 10, b = 15
Using these values in the shortcut, we get:
Required time =
10 x 15 / 10 + 15
=
150 / 25
= 6
Hence, tank will get empty in 6 hours.

13. Two pipes A and B can fill a tank in 10 hours and 15 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
  A.  6 hours
  B.  4 hours
  C.  9 hours
  D.  7 hours
     
   
View Answer

Shortcut:
If a pipe can fill a tank a hours and another can fill the same tank in b hours, then the net part filled in 1 hour, when both the pipes are opened
1 / a
+
1 / b

Therefore, Time taken to fill the tank =
ab / a + b

Here, a = 10, b = 15
Using these values in the shortcut, we get:
Required time =
10 x 15 / 10 + 15
=
150 / 25
= 6
Hence, tank will get empty in 6 hours.

14. Pipe A can fill a tank in 10 hours. Due to a leak in the bottom, it is filled in 15 hours. If the tank is full, how much time will the leak take to empty it?
  A.  20 hours
  B.  30 hours
  C.  25 hours
  D.  35 hours
     
   
View Answer

Shortcut:
A pipe can fill a tank in m hours. Due to a leak in the bottom it is filled in n hours. If the tank is full, the time taken by leak to empty the tank is
mn / n − m
hours
Here, m = 10, n = 15
Using these values in the shortcut, we get:
Required time =
10 x 15 / 15 − 10
=
150 / 5
= 30
Hence, the leak will empty the tank in 30 hours.

15. A cistern is normally filled in 8 hours but takes 2 hours loner to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in:
  A.  30 hours
  B.  25 hours
  C.  20 hours
  D.  40 hours
     
   
View Answer

Shortcut:
A pipe can fill at ank in m hours. Due to a leak in the bottom it is filled in n hours. If the tank is full, the time taken by leak to empty the tank is
mn / n − m
hours
Here, m = 8, n = 10 (8 + 2)
Using these values in the shortcut, we get:
Required time =
8 x 10 / 10 − 8
=
80 / 2
= 40
Hence, the leak will empty the tank in 40 hours.

16. Pipe A can fill a tank in 20 hours while pipe "B alone can fill it in 30 hours and pipe C can empty the full tank in 40 hours. If all the pipes are opened together, how much time will be needed to make the tank full?
  A.  17
1 / 7
hours
  B.  7
3 / 8
hours
  C.  4
8 / 7
hours
  D.  8
7 / 4
hours
     
   
View Answer

Shortcut:
If a pipe fills a tank in 'a' hours and another fills the same tank in 'b' hours, but a third one empties the ful tank in c hours, and all of them are opened together, the net part filed in 1 hour is
1 / a
+
1 / b
−
1 / c

Therefore, Time taken to fill the tank is
a x b x c / bc + ca − ab

Here, a = 20, b = 30, c = 40
Using these values in the shortcut, we get:
Required time =
20 x 30 x 40 / 30 x 40 + 40 x 20 − 20 x 30

=
20 x 30 x 40 / 1200 + 800 − 600

=
20 x 30 x 40 / 2000 − 600

=
20 x 30 x 40 / 1400

=
20 x 3 x 4 / 14
=
20 x 3 x 2 / 7
=
120 / 7
= 17
1 / 7

Hence, the tank will get full in 17
1 / 7
hours.

17. Tap A can fll a water tank in 25 mintutes, tap B can fill the same tank in 40 minutes and tap C can empty the tank in 30 minutes. If all the three taps are opened together, in how many minutes will the tank be completely filled up or emptied?
  A.  31
19 / 11
minutes
  B.  34
13 / 19
minutes
  C.  31
11 / 19
minutes
  D.  29
13 / 17
minutes
     
   
View Answer

Shortcut:
If a pipe fills a tank in 'a' hours and another fills the same tank in 'b' hours, but a third one empties the ful tank in c hours, and all of them are opened together, the net part filed in 1 hour is
1 / a
+
1 / b
−
1 / c

Therefore, Time taken to fill the tank is
a x b x c / bc + ca − ab

Here, a = 25, b = 40, c = 30
Using these values in the shortcut, we get:
Required time =
25 x 40 x 30 / 40 x 30 + 25 x 30 − 25 x 40

=
25 x 40 x 30 / 1200 + 750 − 1000

=
25 x 40 x 30 / 1950 − 1000

=
25 x 40 x 30 / 950

=
5 x 40 x 3 / 19
=
600 / 19
= 31
11 / 19

Hence, the tank will get full in 31
11 / 19
hours.

18. A cistern has 3 pipes, A, B and C. A and B can fill it in 2 hours and 3 hours respectively. C is a waste pipe. If all the 3 pipes be opened at once, 7/30 of the cistern will be filled up in 30 minutes. In what time can C empty the full cistern?
  A.  8
5 / 3
hours
  B.  2
8 / 11
hours
  C.  4
3 / 5
hours
  D.  7
3 / 11
hours
     
   
View Answer

Shortcut:
If a pipe fills a tank in 'a' hours and another fills the same tank in 'b' hours, but a third one empties the ful tank in c hours, and all of them are opened together, the net part filed in 1 hour is
1 / a
+
1 / b
−
1 / c

Therefore, Time taken to fill the tank is
a x b x c / bc + ca − ab

Since
7 / 30
of the cistern will be filled up in
1 / 2
hour.
∴ The whole of the cistern will be filled up in
1 / 2
x
30 / 7
=
15 / 7
hours
Here, a = 2, b = 3, c = 30, Time =
15 / 7

Using these values in the shortcut, we get:
Time =
2 x 3 x c / 3c + 2c − 2 x 3

15/7 =
6c / 5c − 6

15(5c − 6)= 7(6c)
75c − 90 = 42c
75c − 42c = 90
33c = 90
c =
90 / 33
=
30 / 11
= 2
8 / 11

Hence, C can empty tank in 2
8 / 11
hours.

19. Two pipes A and B can fill a cistern in 10 minutes and 20 minutes respectively. There is alo an outlet C. If all the three pipes are opened together, the tank is full in 40 minutes. How much time will be taken by "C to empty the full tank?
  A.  9 minutes
  B.  7 minutes
  C.  3 minutes
  D.  8 minutes
     
   
View Answer

Shortcut:
Two pipes X and Y can fill a cistern in 'a' hour and 'b' hour respectively. There is also an outlet Z. If all the three pipes are opened together, the tank is full in T hours, then the time taken by Z to empty the full tank is
a x b x T / bT + aT − ab

Here, a = 10, b = 20, T = 40
Using these values in the shortcut, we get:
Required time =
10 x 20 x 40 / 20 x 40 + 10 x 40 − 10 x 20

=
10 x 20 x 40 / 800 + 400 − 200

=
10 x 20 x 40 / 1200 − 200

=
10 x 20 x 40 / 1000
= 2 x 4 = 8
Hence, C can empty tank in 8 minutes.

20. In what time would a cistern be filled by three pipes whose diameters are 1 cm, 1
1 / 3
cm, 2 cm, running together, when the largest alone fill it in 122 minutes, the amount of water flowing in by each pipe being proportional to the square of its diameter?
  A.  63 minutes
  B.  67 minutes
  C.  72 minutes
  D.  75 minutes
     
   
View Answer

Shortcut:
A cistern is filled by three pipes whose diametres are a cm, b cm and c cm respectively (where, a < b < c). Three pipes are running together. If the largest pipe alone will fill it in Z minutes and the amount of water flowing in by each pipe being proportional to the square of its diametre, then the time in which the cistern will be filled by the three pipes is
Z x c2 / a2 + b2 + c2
minutes.
Here, Z = 122, a = 1, b = 4/3, c = 2
Using these values in the shortcut, we get:
Required time =
122 x 22 / 12 + 4/32 + 22

=
122 x 4 / 1 + 16/9 + 4

=
122 x 4 / (9 + 16 + 36)/9

=
122 x 4 x 9 / 61
= 2 x 4 x 9 = 72
Hence, the required time is 72 minutes.

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