Pipe and Cistern are one of the most important topics in IBPS PO Clerk & SBI exams. Time is the main factor in competitive exams. If you manage your time then you can do well in those exams. Most of us skip that part.
Here in this post we give some examples on Pipe and Cistern shortcut tricks. These shortcut tricks cover all sorts of tricks on Pipe and Cistern. Readers are requested to carefully read all shortcut examples. You can understand shortcut tricks on Pipe and Cistern by these examples.
Here in this post we give some examples on Pipe and Cistern shortcut tricks. These shortcut tricks cover all sorts of tricks on Pipe and Cistern. Readers are requested to carefully read all shortcut examples. You can understand shortcut tricks on Pipe and Cistern by these examples.
Pipe and Cistern problems are similar to time and work problems. A pipe is used to fill or empty the tank or cistern.
- Inlet Pipe : A pipe used to fill the tank or cistern is known as Inlet Pipe.
- Outlet Pipe : A pipe used to empty the tank or cistern is known as Outlet Pipe.
Some Basic Formulas
- If an inlet pipe can fill the tank in x hours, then the part filled in 1 hour = 1/x
- If an outlet pipe can empty the tank in y hours, then the part of the tank emptied in 1 hour = 1/y
- If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours ( where y > x), then on opening both the pipes, the net part filled in 1 hours = ( 1 / x – 1 / y ).
- If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours ( where x > y), then on opening both the pipes, the net part emptied in 1 hours = ( 1 / y – 1 / x ).
Shortcuts
Rule 1 : Two pipes can fill (or empty) a cistern in x and y hours while working alone. If both pipes are opened together, then the time taken to fill (or empty) the cistern is given by =
Rule 1 : Two pipes can fill (or empty) a cistern in x and y hours while working alone. If both pipes are opened together, then the time taken to fill (or empty) the cistern is given by =
Rule 2 : Three pipes can fill (or empty) a cistern in x, y and z hours while working alone. If all the three pipes are opened together, the time taken to fill (or empty) the cistern is given by =
Rule 3 : If a pipe can fill a cistern in x hours and another can fill the same cistern in y hours, but a third one can empty the full tank in z hours, and all of them are opened together, then
Rule 4 : A pipe can fill a cistern in x hours. Because of a leak in the bottom, it is filled in y hours. If it is full, the time taken by the leak to empty the cistern is
Questions of Pipe and Cistern
1. Two taps A and B can fill a tank in 10 hours and 15 hours respectively. If both the taps are opened together, the tank will be full in ?
Ans : If A can do a piece of work in x hours and B can do a piece of work in y hours.
Then A and B together will do the work in =
Time taken by A = 10 hours
Time taken by B = 15 hours
Time taken by A and B = (15x10 / 15+10) = 6 hours.
2. To fill a cistern, pipes A, B and C take 20 minutes, 15 minute and 12 minutes respectively. The time in minutes that the three pipes together will take to fill the cistern is:
Ans : A can do a piece of work in x minutes
B can do a piece of work in y minutes
C can do a piece of work in z minutes
Minute’s work of each of the three is 1/x +1/y + 1/z
1 minutes work of each of the three pipes = 1/20 + 1/15 + 1/12
= 1/5 or = 5 minutes
3. Two pipes can fill a tank in 10 hours and 12 hours resp. while third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time the tank will be filled?
Ans : Pipe A can fill a tank in x hours and pipe B can fill a tank in y hours and pipe C can empty it in z hours. If all the pipes are operate simultaneously, 1 hours of work of each of the three pipes = 1/x +1/y - 1/z
1 minutes work of each of the three pipes = 1/10 + 1/12 - 1/20 = 15/2 hours
= 7 ½ hour = 7 hours 30 minutes.
4. A cistern can be filled in 9 hours but it takes 10 hours due to a leak in its bottom. If the cistern is full, then the time that the leak will take to empty it is:
Ans : If A can fill a tank in x hours and B can fill a tank in y hours. Then the tank will be filled (empty) in = (xy / y-x) hours
Time taken by A = 9 hours
Time taken by B = 10 hours
Time taken by A and B = (9x10 / 10-9) = 90 hours.
5. An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 ½ hours to fill the tank. The leak can drain out of all the water of the tank in:
Ans : If A can fill a tank in x hours and B can fill a tank in y hours. Then the tank will be filled (empty) in = (xy / y-x) hours
Time taken = 3 hours
Time taken = 3 ½ hours
Time taken by A and B = (3 x 3 ½ / 3 ½ - 3) = 21 hours
6. Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and A is closed after 3 minutes. How much further time would it take for B to fill the bucket?
Ans : Total work (to fill or empty) = I part + II part = 1
Find Ist part and subtract it from ‘1’ , then multiply the required section value to find the answer.
For 3 minutes (I part) = 3(1/12 + 1/15) = 9/20
Remaining part = 1- 9/20 = 11/20
Tap B fill the bucket in = 11/20 - 15
= 33/4 = 8 ¼ hours = 8 hours 15 seconds.
7. A tank can be filled by a tap in 20 minutes and by another tap in 60 minutes. Both taps are kept open for 10 minutes and then the first tap is shut off. After this, the tank will be completely filled in:
Ans : Total work (to fill or empty) = I part + II part =1
For 10 minutes (I part) = 10(1/20 + 1/60) = 4/6 = 2/3
Remaining part = 1- ( I part)
= 1 - 2/3 = 1/3
The tank will be complete by filled in (B only, after 10 minutes) = 1/3 x 60 = 20 minutes.
8. If two pipes function simultaneously the reservoir will be filled in 12 hours, one pipe fills the reservoir 10 hours faster than the other. How many hours it takes the second pipe to fill the reservoir?
Ans : Let the reservoir be filled by faster pipe in X hours, therefore the second pipe will fill it in (x+10) hours.
= 1/X + 1/ X + 10 = 1/12
X = 20
The second pipe can take (X +10) = 20 + 10 = 30 hours, to fill the reservoir.
Ans : A can do a piece of work in x minutes
B can do a piece of work in y minutes
C can do a piece of work in z minutes
Minute’s work of each of the three is 1/x +1/y + 1/z
1 minutes work of each of the three pipes = 1/20 + 1/15 + 1/12
= 1/5 or = 5 minutes
3. Two pipes can fill a tank in 10 hours and 12 hours resp. while third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time the tank will be filled?
Ans : Pipe A can fill a tank in x hours and pipe B can fill a tank in y hours and pipe C can empty it in z hours. If all the pipes are operate simultaneously, 1 hours of work of each of the three pipes = 1/x +1/y - 1/z
1 minutes work of each of the three pipes = 1/10 + 1/12 - 1/20 = 15/2 hours
= 7 ½ hour = 7 hours 30 minutes.
4. A cistern can be filled in 9 hours but it takes 10 hours due to a leak in its bottom. If the cistern is full, then the time that the leak will take to empty it is:
Ans : If A can fill a tank in x hours and B can fill a tank in y hours. Then the tank will be filled (empty) in = (xy / y-x) hours
Time taken by A = 9 hours
Time taken by B = 10 hours
Time taken by A and B = (9x10 / 10-9) = 90 hours.
5. An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 ½ hours to fill the tank. The leak can drain out of all the water of the tank in:
Ans : If A can fill a tank in x hours and B can fill a tank in y hours. Then the tank will be filled (empty) in = (xy / y-x) hours
Time taken = 3 hours
Time taken = 3 ½ hours
Time taken by A and B = (3 x 3 ½ / 3 ½ - 3) = 21 hours
6. Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and A is closed after 3 minutes. How much further time would it take for B to fill the bucket?
Ans : Total work (to fill or empty) = I part + II part = 1
Find Ist part and subtract it from ‘1’ , then multiply the required section value to find the answer.
For 3 minutes (I part) = 3(1/12 + 1/15) = 9/20
Remaining part = 1- 9/20 = 11/20
Tap B fill the bucket in = 11/20 - 15
= 33/4 = 8 ¼ hours = 8 hours 15 seconds.
7. A tank can be filled by a tap in 20 minutes and by another tap in 60 minutes. Both taps are kept open for 10 minutes and then the first tap is shut off. After this, the tank will be completely filled in:
Ans : Total work (to fill or empty) = I part + II part =1
For 10 minutes (I part) = 10(1/20 + 1/60) = 4/6 = 2/3
Remaining part = 1- ( I part)
= 1 - 2/3 = 1/3
The tank will be complete by filled in (B only, after 10 minutes) = 1/3 x 60 = 20 minutes.
8. If two pipes function simultaneously the reservoir will be filled in 12 hours, one pipe fills the reservoir 10 hours faster than the other. How many hours it takes the second pipe to fill the reservoir?
Ans : Let the reservoir be filled by faster pipe in X hours, therefore the second pipe will fill it in (x+10) hours.
= 1/X + 1/ X + 10 = 1/12
X = 20
The second pipe can take (X +10) = 20 + 10 = 30 hours, to fill the reservoir.
9. 12 buckets of water fill a taken when the capacity of each bucked is 13.5 liter. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres ?
Ans : Here the tank is same
Number of buckets x capacity of bucket = Number of buckets x capacity of bucket
The capacity of the tank is same,
N1 x W1 = N2 x W2
N1 = No. of Buckets W1 = Capacity of liters in the buckets
N2 = No. of Buckets W2 = Capacity of liters in the buckets
Ans : Here the tank is same
Number of buckets x capacity of bucket = Number of buckets x capacity of bucket
The capacity of the tank is same,
N1 x W1 = N2 x W2
N1 = No. of Buckets W1 = Capacity of liters in the buckets
N2 = No. of Buckets W2 = Capacity of liters in the buckets
= 12 x 13.5 = N2 x 9
= N2 = 18
10. Bucket p has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the empty drum. How many turns it will take for both the buckets p and q having each turn together to fill the empty drum.
Ans : Bucket P has thrice the capacity as bucket Q
Q = 3 P
P takes 60 turns
Q takes = 180 turns
P and Q takes = (180x 60 / 60+180) = 45 turns.
Ans : Bucket P has thrice the capacity as bucket Q
Q = 3 P
P takes 60 turns
Q takes = 180 turns
P and Q takes = (180x 60 / 60+180) = 45 turns.
11. Two pipes A and B fill a tank in 15 hours and 20 hours respectively while a third pipe c can empty the full tank in 25 hours. All the three pipes are opened in the beginning, after 10 hours, c is closed. In how much time, will the tank be full ?
Ans :
A B C
15 20 -25
For 10 hours = 10(1/15 +1/20 - 1/25) = 23/30 ( Part I)
Remaining part =1- 23/30 = 7/30
(A+B)’s 1 hour work
= 1/15 + 1/20 = 4/60 + 3/60 = 7/60
Therefore = 7/30 x 60/7 = 2 hours
Hence 10+2 = 12 hours
12. Two pipes A and B and can fill a cistern in 12 minutes and 15 minutes respectively but a third pipe c can empty the full tank in 6 minutes. A and B are kept open for 5 minutes in the beginning and then c is also opened. In what time is the cistern emptied
Ans : 1/x +1/y - 1/z
For 5 minutes = 5(1/12 +1/15) = 3/4
When all the three pipes are opened = 1/12 + 1/15 – 1/6
= -1/60 ("-" means emptying)
Empty the cistern in 1 min is 1/60
Therefore 3/4 will emptied in 3/4 x 60 = 45 minutes.
13. Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the cistern is:
Ans : A+B+C = 1/6
For 2 hours = 2 (1/6) = 1/3
Remaining = 2/3
(A+B)’s 7 hours work = 2/3
(A+B)’s 1 hours work = 2/21
C’s 1 hour work = (A+B+C)’s work – (A+B)’s work = 1/6 - 2/21
= 9/126 = 1/14
C alone can fill the tank in 14 hours
14. A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water are the rate of 6 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold ?
Ans : Time taken to fill the tank is 1/8
Time taken to empty the taken is 1/12
Work done by the inlet in 1 hour = (1/8 + 1/12) = 1/24
Work done by the inlet in 1 minute = 1/24 x 1/60 = 1/1440
Therefore Volume = 1440 x 6 liters = 8640 liters
Ans :
A B C
15 20 -25
For 10 hours = 10(1/15 +1/20 - 1/25) = 23/30 ( Part I)
Remaining part =1- 23/30 = 7/30(A+B)’s 1 hour work
= 1/15 + 1/20 = 4/60 + 3/60 = 7/60
Therefore = 7/30 x 60/7 = 2 hours
Hence 10+2 = 12 hours
12. Two pipes A and B and can fill a cistern in 12 minutes and 15 minutes respectively but a third pipe c can empty the full tank in 6 minutes. A and B are kept open for 5 minutes in the beginning and then c is also opened. In what time is the cistern emptied
Ans : 1/x +1/y - 1/z
For 5 minutes = 5(1/12 +1/15) = 3/4
When all the three pipes are opened = 1/12 + 1/15 – 1/6
= -1/60 ("-" means emptying)
Empty the cistern in 1 min is 1/60
Therefore 3/4 will emptied in 3/4 x 60 = 45 minutes.
13. Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the cistern is:
Ans : A+B+C = 1/6
For 2 hours = 2 (1/6) = 1/3
Remaining = 2/3
(A+B)’s 7 hours work = 2/3
(A+B)’s 1 hours work = 2/21
C’s 1 hour work = (A+B+C)’s work – (A+B)’s work = 1/6 - 2/21
= 9/126 = 1/14
C alone can fill the tank in 14 hours
14. A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water are the rate of 6 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold ?
Ans : Time taken to fill the tank is 1/8
Time taken to empty the taken is 1/12
Work done by the inlet in 1 hour = (1/8 + 1/12) = 1/24
Work done by the inlet in 1 minute = 1/24 x 1/60 = 1/1440
Therefore Volume = 1440 x 6 liters = 8640 liters
Post a Comment