Pipes and Cisterns.25
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Transcript of Pipes and Cisterns.25
PIPES AND CISTERNS
1. Two taps A and B can fill a tank in 10 hours and 15 hours and 15
hours respectively. If both the taps are opened together, the tank will be full
in ?
Ans:6hrs
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
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 hours
Answer with Explanation:
Time taken by A = 10 hours
Time taken by B = 15 hours
Time taken by A and B =
= = 6 hours.
Pipes and Cisterns, BU Page 1 www.aptitudecoach.com
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:5
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
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
Answer with Explanation:
1 minutes work of each of the three pipes
= 1/20 + 1/15 + 1/12
= =
= 1/5
= 5 minutes
Pipes and Cisterns, BU Page 2 www.aptitudecoach.com
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;7 hrs 30 mins
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
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
Answer with Explanation:
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.
Pipes and Cisterns, BU Page 3 www.aptitudecoach.com
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:90 hrs
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
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 hours
Answer with Explanation:
Time taken by A = 9 hours
Time taken by B = 10 hours
Time taken by A and B =
= 90 hours.
Pipes and Cisterns, BU Page 4 www.aptitudecoach.com
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:21 hrs
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
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 hours
Answer with Explanation:
Time taken = 3 hours
Time taken = 3 ½ hours
Time taken by A and B =
=
=
= 21 hours
Pipes and Cisterns, BU Page 5 www.aptitudecoach.com
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 8 min 15 sec
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Total work (to fill or empty) = I part + II part =1
Find I st part and subtract it from ‘1’ , then multiply the required
section value to find the answer.
Answer with Explanation:
For 3 minutes (I part)
= 3
= 3
= 3 = 9/20
Remaining part
= 1- 9/20 = 11/20
Tap B fill the bucket in
= -15
= 33/4 = 8 ¼ hours
= 8 hours 15 seconds.
Pipes and Cisterns, BU Page 6 www.aptitudecoach.com
7. A tank can be filled by a tap in 20 minutes and by another tap in 60
mintues. Both taps are kept open for 10 mintues and then the first tap is shut
off. After this, the tank will be completely filled in:
Ans:20 min
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Total work (to fill or empty) = I part + II part =1
Answer with Explanation:
For 10 minutes (I part)
= 10
= 10
= 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.
Pipes and Cisterns, BU Page 7 www.aptitudecoach.com
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:30 hours
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Taken unknown value as x and use
Answer with Explanation:
Let the reservoir be filled by forst pipe in x hours, therefore the second pipe
will fill it in (x+10) hours.
1/x + 1/ x+10 = 1/12
= 1/12
12 (10+2x) = x2 +10x
x2 +10x – 24x – 120 = 0
x2 – 14x – 120 = 0
(x-20) (x+6) = 0
x = 20 (x should nor –ve)
The second pipe can take (x+10) = 20 + 10 = 30 hours, to fill the
reservoir.
Pipes and Cisterns, BU Page 8 www.aptitudecoach.com
9. One tap can fill a cistern in 2 hours and another tap can empty the
cistern in 3 hours. How long will they take to fill the cistern if both the taps
are opened?
Ans: 6hours
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Pipe A can fill a tank in ‘x’ hours and pipe B can empty it in ‘y’ hours. If
both the pipes opened together, the tank will be filled in hours.
Answer with Explanation:
Time taken to fill the tank = 2 hours
Time taken to empty the tank = 3 hours
Time taken to fill the cistern =
= 6 hours.
Pipes and Cisterns, BU Page 9 www.aptitudecoach.com
10. 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:18
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Here the tank is same
Number of buckets X capacity of bucket = Number of buckets X
capacity of bucket
Answer with Explanation:
The capacity of the tank is same,
N1 X W1 = N2X 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 X9
= N2 = = 54/3
= N2 = 18
Pipes and Cisterns, BU Page 10 www.aptitudecoach.com
11. 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:
Answer:45
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
=
Answer with Explanation:
Bucket P has thrice the capacity as bucket Q
Q= 3 P
P takes 60 turns
Q takes = 180 turns
P and Q takes =
=
= 45 turns.
Pipes and Cisterns, BU Page 11 www.aptitudecoach.com
12. 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:12 hrs
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
1/x +1/y - 1/z Part I and Part II = 1
Answer with Explanation:
A B C
15 20 -25
For 10 hours = 10
= 10
= 10
= 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
Pipes and Cisterns, BU Page 12 www.aptitudecoach.com
13. 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 mintues.
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:45 mints
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
1/x +1/y - 1/z
Answer with Explanation:
A B C
12 15 -6
For 5 minutes = 5
= 5
= ¾
When all the three pipes are opened = 1/12 + 1/15 – 1/6
= 15/180 + 12/180 – 30/180
= -3/180 = -1/60 (-means emptying)
Empty the cistern in 1 min is 1/60
Therefore ¾ will emptied in ¾ X 60 = 45 minutes.
Pipes and Cisterns, BU Page 13 www.aptitudecoach.com
14. Three pipes A, B and C can fill a tank in 6 hours. After working at it
together for 2hours, 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:
Answer:14
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
C’s work = (A+B+C)’s work – (A+B)’s work
Answer with Explanation:
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
Pipes and Cisterns, BU Page 14 www.aptitudecoach.com
15. 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: 8,640
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Work done = 1/x – 1/y
Time X number of liters
Answer with Explanation:
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 = =
= = 1/24
Work done by the inlet in 1 minute = 1/24 X 1/60 = 1/1440
Therefore Volume = 1440 X6 liters
= 8640 liters
Pipes and Cisterns, BU Page 15 www.aptitudecoach.com
16. A leak in the bottom of a tank can empty the full tank in 6 hours. An
inlet pipe fills water at the rate of 4 litres a minute. When the tank is full the
inlet is opened and due to the leak the tank is empty in 8 hours. The capacity
of the tank in litres is : Ans 5760.
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Work done = 1/x – 1/y
Time X number of liters
Answer with Explanation:
Time taken to fill the tank is 1/6 hour (Time taken to empty = time taken to
full)
Time taken to empty the tank is 1/8
Work done by the inlet in 1 hour = (1/6 – 1/8)
= = 2 / 48 = 1/24
For 1 minute = 1/24X1/60 = 1/1440
An inlet pipe fill water at the rate of 4 liters a minute = 1440 X 4 = 5760
liters
Pipes and Cisterns, BU Page 16 www.aptitudecoach.com
17. A tap can fill a tank in 16 minutes and another can empty it in 8
minutes. If the tank is already half-full and both tanks are opened together,
the tank will be :
Ans: emptied in 8 min
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Work done = 1/x – 1/y
Answer with Explanation:
Time taken to fill the tank in = 1/16 min
Time taken to empty the tank in = 1/8 min
Work done by both in 1 min = (1/16 – 1/8)
= = -8 / 16X8
= -1/16 (-ve means empty)
Now full tank will be emptied by them in 16 min
Half tank will be emptied in 8 min.
Pipes and Cisterns, BU Page 17 www.aptitudecoach.com
18. A cistern has two taps which fill it in 12 min and 15 min respectively.
There is also a waste pipe in the cistern. When all the three are opened, the
empty cistern is full in 20 mintues. How long will waste pipe take to empty
the full cistern ?
Ans;10 min
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
C’s work = (A+B+C)’s work – (A+B)’s work
A + B = 1/x+1/y
Answer with Explanation:
To fill the cistern = (1/12 + 1/15) =
= 3/20
Work done by waste pipe in 1 min
= work done by all the three taps – work done by two taps (fill)
= 1/20 – 3/20 = -2/20 = -1/10 (-ve means empty)
Waste pipe will empty the full cistern in 10 minutes.
Pipes and Cisterns, BU Page 18 www.aptitudecoach.com
19. Two pipes A and B can fill a cistern in 12 minutes and 15 mint
respectively. If both the pipes are opened together, then after how much time
B should be closed so that the tank is full in 9 minutes?
Ans 4 min
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Let B be closed after x minutes.
I part + II part = 1
I part = Cistern filled by (A+B) in x min
II part = Cistern filled by A in (9-x) minutes
Answer with Explanation:
+ (9-x) X 1/12 = 1
= 1
x - x/12 = 1-9/12
= 3/12
7x – 4x = 12
3x = 12
X = 4
So, B must be closed after 4 minutes.
Pipes and Cisterns, BU Page 19 www.aptitudecoach.com
20. A water tank is two – fifth full. Pipe A can fill a tank in 10 minutes and
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?
Answer : 6 minutes
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
AB/B-A
Answer with Explanation:
Water level in the tank is 2/5
Both the pipes are open = = =
Therefore 2/5 X15 = 6 minutes
Pipes and Cisterns, BU Page 20 www.aptitudecoach.com
21. Pipes A and B take 20 and 30 minutes to fill a tank respectively. The 2
together will take :
Answer : 12
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
AB/A+ B
Answer with Explanation:
A = 20
B = 30
Together = A+B/AB
=
= =
Therefore 12 minutes.
Pipes and Cisterns, BU Page 21 www.aptitudecoach.com
22. 2 pipes A and B can fill a tank in 36 hours and 45 hours respectively. If
both are opened simultaneously, how much time will be taken to fill the
tank?
Answer : 20 hours
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Time taken to fill the tank = A+B/AB
Answer with Explanation:
A = 36
B = 45
=
=
= 20 hours
Pipes and Cisterns, BU Page 22 www.aptitudecoach.com
23.Two pipes A and B can fill a tank in 6 hours and 4 hours respectively.
If they are opened on alternate hours and if pipe A is opened first, in
how many hours, the tank shall be full ?
Ans: 5 hours
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
It’s an alternate hour’s problem
A’s 1hour work = 1/6
B’s 1 hour work = ¼
A + B means 2 hours of work
Answer with Explanation:
(A+B)’s 2 hours work when opened alternately = =
(A+B)’s 4 hours work when opened alternately = 2 (5/12) = 5/6
Remaining = 1-5/6 =1/6
It is A’s turn and 1/6 part is filled by A in 1 hour
Total time taken to fill the tank = (4+1) hours
= 5 hours
Pipes and Cisterns, BU Page 23 www.aptitudecoach.com