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1. Pipes and Cisterns

2. • A can fill the cistern in m hours , then
part of the cistern filled by A = th part
• B can empty the cistern in n hours , then
part of the cistern filled by A = th part
• Work done by A + B per day = =
Time taken by A and B =
Basics :
NOTE :
Work done per day and total number of hours taken to fill or empty the cistern
are reciprocals (not inversely proportional).
A, B are pipes

3. 1. Two filling pipes A and B can fill a cistern in 20 min and 30 min
respectively. Both the pipes are opened together. But pipe B is closed after
few minutes. After how many minutes is pipe B is closed if cistern is full in
16 min?
2. A filling pipe A can fill an empty cistern in 24 min and an emptying pipe B,
can empty the same full cistern in 32 min. Both the pipes A and B are
opened together but pipe B was closed after few minutes. After how many
minutes was pipe B closed, if the cistern is full in 30 min?
3. A filling pipe A can fill an empty cistern in 27 min and an emptying pipe B
can empty the same full cistern in 45 min. But the pipes A and B are
opened together, but pipe B was closed after 15min. What is the total time
taken to fill the cistern?

4. Two filling pipes A and B can fill an empty cistern in 30 min and 60min
respectively. While a third pipe C can empty the same full cistern in 15
min. Initially both the pipes A and B are opened for the first 15 min and
then pipe C was also opened. What is the time taken to fill or empty
the cistern after pipe C was opened?
A cistern has a leakage which can empty the full cistern in 8hrs. When
the cistern was full, a tap was turned on, which empty 5 lit of water per
minute from the cistern and the cistern is now emptied in 2 hrs. find
the capacity of the cistern?
5.
4.

5. Two filling pipes A and B can fill a cistern in 20 min and 30 min respectively.
Both the pipes are opened together. But pipe B is closed after few minutes.
After how many minutes is pipe B is closed if cistern is full in 16 min?
Ans :
A – B --
A has been opened till the cistern is full
 Part of cistern is filled by A is 16 =
 Remaining part is filled by B
 Time taken by pipe B is = 6 min.
1.
6 min after pipe B is closed.

6. A filling pipe A can fill an empty cistern in 24 min and an emptying pipe B,
can empty the same full cistern in 32 min. Both the pipes A and B are
opened together, but pipe B was closed after few minutes. After how
many minutes was pipe B closed, if the cistern is full in 30 min?
2.
Ans :
A – B --
A has been opened till the cistern is full
 Part of cistern is filled by A is =
 part is extra filled by A which is emptied by B
 Time taken by pipe B is 2 = 8 min.
8 min after pipe B is closed.

7. A filling pipe A can fill an empty cistern in 27 min and an emptying pipe
B can empty the same full cistern in 45 min. But the pipes A and B are
opened together, but pipe B was closed after 15min. What is the total
time taken to fill the cistern?
3.
The total time taken to fill the cistern by A = 36min
Ans :
A – B --
A has been opened till the cistern is full
 Part of cistern is emptied by B is =
 1 + part is filled by A .. Time taken by pipe A is = 36 min.

8. Two filling pipes A and B can fill an empty cistern in 30 min and 60min
respectively. While a third pipe C can empty the same full cistern in 20
min. Initially both the pipes A and B are opened for the first 15 min and
then pipe C was also opened. What is the time taken to empty the
cistern after pipe C was opened?
4.
Ans :
A – B -- C --
A has been opened till the cistern is full
 Part of cistern is filled by A is = and B = =
 th part is filled by A and B .. Time taken by pipe C is = 15 min.
Time taken to empty the cistern after pipe C was opened is 15 min

9. A cistern has a leakage which can empty the full cistern in 8hrs. When
the cistern was full, a tap was turned on, which admits 5 lit of water per
minute in the cistern and the cistern is now emptied in 2 hrs. find the
capacity of the cistern?
5.
Ans :
leakage can empty the cistern in 8 hrs
 Part of the cistern emptied by leakage is th part per hour.
 For 2 hrs, it will empty th part.
 Remaining th part is equal to 5lit = 600lit .
th = 600
= 800
Capacity of the cistern is 800 litres

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Problems for practice are given in the description of the video.