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Pipes and Cisterns, Page 1
COURSE MODULE NAME
PIPES AND CISTERNS
Pipes and Cisterns, Page 2
Basic formulas
1. Inlet:
A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as aninlet.
Outlet:
A pipe connected with a tank or cistern or reservoir, emptying it, is known as anoutlet.
2. If a pipe can fill a tank in x hours, then:
part filled in 1 hour =1.
x
3. If a pipe can empty a tank in y hours, then:
part emptied in 1 hour =1.
y
4. If a pipe can fill a tank in x hours and another pipe can empty the full tank in yhours (where y > x), then on opening both the pipes, then
the net part filled in 1 hour =1-1
.x y
5. If a pipe can fill a tank in x hours and another pipe can empty the full tank in yhours (where y > x), then on opening both the pipes, then
the net part emptied in 1 hour = 1-1 .
6.Time for filling , (Filling pipe is bigger in size.)
F = (e * f)/(e - f)
Pipes and Cisterns, Page 3
7.Time for emptying , (emptying pipe is bigger in size.)
E = (f * e)/(f - e)
8.Pipes 'A' & 'B' can fill a tank in f1hrs & f2hrs respectively.Another pipe 'C' can emptythe full tank in 'e'hrs.If the three pipes are opened simultaneously then the tank is filled in
F = L/[(L/f1) + (L/f2) - (L/e)]
9.Two taps 'A' & 'B' can fill a tank in 't1' & 't2' hrs respectively.Another pipe 'C' canempty the full tank in 'e'hrs.If the tank is full & all the three pipes are openedsimultaneously . Then the tank will be emptied in,
E = L/[(L/e) - (L/f1) - (L/f2)]
10.A filling tap can fill a tank in 'f'hrs.But it takes 'e'hrs longer due to a leak at thebottom.The leak will empty the full tank in ,
E = [t(f * e) * tf]/[t(f + e) - tf]
11.Capacity of the tank is ,
F = (f * e)/(e - f)
Pipes and Cisterns, Page 4
Solved Examples
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
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 inyx
xy
hours
Answer with Explanation:
Time taken by A = 10 hours
Time taken by B = 15 hours
Time taken by A and B =1015
1015
X
=25
1015X= 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:5
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
=60
543 =
60
12
= 1/5
Pipes and Cisterns, Page 5
= 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;7 hrs 30 mins
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
=60
356 =
60
8
=15
2
= 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:90 hrs
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) inyx
xy
hours
Answer with Explanation:
Time taken by A = 9 hours
Time taken by B = 10 hours
Time taken by A and B =910
109
x
Pipes and Cisterns, Page 6
= 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:21 hrs
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) inyx
xy
hours
Answer with Explanation:
Time taken = 3 hours
Time taken = 3 ½ hours
Time taken by A and B =3
2
13
2
133
x
=3
2
72
73
x
=
2
672
73
x
= 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 8 min 15 sec
Basic Formula:
Total work (to fill or empty) = I part + II part =1
Pipes and Cisterns, Page 7
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
15
1
12
1
= 3
1215
1215
X
= 3
20
3= 9/20
Remaining part
= 1- 9/20 = 11/20
Tap B fill the bucket in
=20
11-15
= 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 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
Basic Formula:
Total work (to fill or empty) = I part + II part =1
Answer with Explanation:
For 10 minutes (I part)
= 10
60
1
20
1
Pipes and Cisterns, Page 8
= 10
60
4
= 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:30 hours
Basic Formula:
Taken unknown value as x and useyx
xy
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
)10(
10
xx
xx= 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, Page 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
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 inyx
xy
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 =13
32
X
= 6 hours.
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:18
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
Pipes and Cisterns, Page 10
= 12 X 13.5 = N2 X9
= N2 =9
5.1312X= 54/3
= 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:
Answer:45
Basic Formula:
yx
xy
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 =18060
60180
X
=240
60180X
= 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:12 hrs
Basic Formula:
1/x +1/y - 1/z Part I and Part II = 1
Answer with Explanation:
A B C
15 20 -25
Pipes and Cisterns, Page 11
For 10 hours = 10
25
1
20
1
15
1
= 10
300
12
300
15
300
20
= 10
300
23
= 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 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
Basic Formula:
1/x +1/y - 1/z
Answer with Explanation:
A B C
12 15 -6
For 5 minutes = 5
15
1
12
1
= 5
180
27
= 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)
Pipes and Cisterns, Page 12
Empty the cistern in 1 min is 1/60
Therefore ¾ will emptied in ¾ X 60 = 45 minutes.
13. 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
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
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: 8,640
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 =
12
1
8
1=
812
812
X
Pipes and Cisterns, Page 13
=812
4
X= 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, Page 14
Exercise problems
1.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.
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)
=86
68
X
= 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
02.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
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)
=816
168
X
= -8 / 16X8
= -1/16 (-ve means empty)
Pipes and Cisterns, Page 15
Now full tank will be emptied by them in 16 min
Half tank will be emptied in 8 min.
03.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
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) =1512
27
X
= 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.
04.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
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:
16
1
12
1x + (9-x) X 1/12 = 1
1212
9
1612
1216 x
Xx
= 1
Pipes and Cisterns, Page 16
x1612
28
x- x/12 = 1-9/12
12412
7 x
x
x = 3/12
7x – 4x = 12
3x = 12
X = 4
So, B must be closed after 4 minutes.
05. 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
Basic Formula:
AB/B-A
Answer with Explanation:
Water level in the tank is 2/5
Both the pipes are open =610
610
X
=
60
4=
15
1
Therefore 2/5 X15 = 6 minutes
06.. Pipes A and B take 20 and 30 minutes to fill a tank respectively. The 2 together will
take :
Answer : 12
Basic Formula:
AB/A+ B
Answer with Explanation:
A = 20
B = 30
Together = A+B/AB
=3020
3020
X
=3020
50
X=
12
1
Pipes and Cisterns, Page 17
Therefore 12 minutes.
07.. 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
Basic Formula:
Time taken to fill the tank = A+B/AB
Answer with Explanation:
A = 36
B = 45
BA
AB
=
4536
4536
X
=81
4536X
= 20 hours
08.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
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 =
4
1
6
1=
24
64
(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, Page 18
8. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes,and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A,B and C discharge chemical solutions P,Q and R respectively. What is the proportionof the solution R in the liquid in the tank after 3 minutes?
A.511
B.611
C.711
D.811
Answer & Explanation
Answer: Option B
Explanation:
Part filled by (A + B + C) in 3 minutes = 31
+1
+1
= 3 x11
=11
.30 20 10 60 20
Part filled by C in 3 minutes =3
.10
Required ratio =3
x20
=6
.10 11 11
9. Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C canempty it in 12 hours. If all the three pipes are opened together, then thetank will be filled in:
A.113
hours17
B.28
hours11
C.39
hours17
D.41hours
2
Answer: Option C
Explanation:
Net part filled in 1 hour1+
1-
1=
17.
5 6 12 60
The tank will be full in60
hours i.e., 39
hours.17 17
Pipes and Cisterns, Page 19
10.A pump can fill a tank with water in 2 hours. Because of la leak, it took 2 hours tofill the tank. The leak can drain all the water of the tank in:
A.41hours
3B.7 hours
C.8 hours D.14 hours
Answer: Option D
Explanation:
Work done by the leak in 1 hour =1-3
=1
.2 7 14
Leak will empty the tank in 14 hrs.
11.Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively.Both pipes are opened. The cistern will be filled in just half an hour, if the B is turnedoff after:A.5 min. B.9 min.C.10 min. D.15 min.
Answer: Option B
Explanation:
Let B be turned off after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.
x2
+1
+ (30 - x).2
= 175 45 75
11x+
(60 -2x)= 1
225 75
11x + 180 - 6x = 225.
Pipes and Cisterns, Page 20
x = 9.
12. A tank is filled by three pipes with uniform flow. The first two pipes operatingsimultaneously fill the tank in the same time during which the tank is filled by thethird pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4hours slower than the third pipe. The time required by the first pipe is:A.6 hours B.10 hoursC.15 hours D.30 hours
Answer: Option C
Explanation:
Suppose, first pipe alone takes x hours to fill the tank .
Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank.
1+
1=
1x (x - 5) (x - 9)x - 5 + x
=1
x(x - 5) (x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x - 15)(x - 3) = 0
x = 15. [neglecting x = 3]
13. Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe canempty 3 gallons per minute. All the three pipes working together can fill the tank in15 minutes. The capacity of the tank is:A.60 gallons B.100 gallonsC.120 gallons D.180 gallons
Answer: Option C
Explanation:
Pipes and Cisterns, Page 21
Work done by the waste pipe in 1 minute =1
-1
+1
15 20 24
=1
-11
15 120
= -1
. [-ve sign means emptying]40
Volume of1
part = 3 gallons.40
Volume of whole = (3 x 40) gallons = 120 gallons.
14. A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as Band B is twice as fast as A. How much time will pipe A alone take to fill the tank?A.20 hours B.25 hoursC.35 hours D.Cannot be determinedE.None of these
Answer: Option C
Explanation:
Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will takexand
xhours respectively to fill the tank.
2 41+
2+
4=
1x x x 57=
1x 5
x = 35 hrs.
15. Two pipes A and B together can fill a cistern in 4 hours. Had they been openedseparately, then B would have taken 6 hours more than A to fill the cistern. Howmuch time will be taken by A to fill the cistern separately?A.1 hour B.2 hoursC.6 hours D.8 hours
Answer: Option C
Explanation:
Pipes and Cisterns, Page 22
Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours.
1+
1=
1x (x + 6) 4x + 6 + x
=1
x(x + 6) 4
x2 - 2x - 24 = 0
(x -6)(x + 4) = 0
x = 6. [neglecting the negative value of x]
16. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipesare used together, then how long will it take to fill the tank?A.12 min B.15 minC.25 min D.50 min
Answer: Option A
Explanation:
Part filled by A in 1 min =1
.20
Part filled by B in 1 min =1
.30
Part filled by (A + B) in 1 min =1
+1
=1
.20 30 12
Both pipes can fill the tank in 12 minutes.
17. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Boththe pipes are opened together but after 4 minutes, pipe A is turned off. What is thetotal time required to fill the tank?A.10 min. 20 sec. B.11 min. 45 sec.C.12 min. 30 sec. D.14 min. 40 sec.
Answer: Option D
Explanation:
Pipes and Cisterns, Page 23
Part filled in 4 minutes = 41
+1
=7
.15 20 15
Remaining part = 1 -7
=8
.15 15
Part filled by B in 1 minute =120
1:
8:: 1 : x
20 15
x =8
x 1 x 20 = 102min = 10 min. 40 sec.
15 3
The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.
18. One pipe can fill a tank three times as fast as another pipe. If together the two pipescan fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tankin:A.81 min. B.108 min.C.144 min. D.192 min.
Answer: Option C
Explanation:
Let the slower pipe alone fill the tank in x minutes.
Then, faster pipe will fill it inxminutes.
31+
3=
1x x 364=
1x 36
x = 144 min.
19. A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutesrespectively. How many minutes will it take to fill the tanker from empty state if B isused for half the time and A and B fill it together for the other half?A.15 min B.20 minC.27.5 min D.30 min
Answer: Option D
Explanation:
Pipes and Cisterns, Page 24
Part filled by (A + B) in 1 minute =1
+1
=1
.60 40 24
Suppose the tank is filled in x minutes.
Then,x 1
+1
= 12 24 40
xx
1= 1
2 15
x = 30 min.
20. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps areopened. What is the total time taken to fill the tank completely?A.3 hrs 15 min B.3 hrs 45 minC.4 hrs D.4 hrs 15 min
Answer: Option B
Explanation:
Time taken by one tap to fill half of the tank = 3 hrs.
Part filled by the four taps in 1 hour = 4 x1
=2.
6 3
Remaining part = 1 -1
=1.
2 22:1:: 1 : x
3 2
x =1x 1 x
3=
3hours i.e., 45 mins.
2 2 4
So, total time taken = 3 hrs. 45 mins.
21. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is openall the time and B and C are open for one hour each alternately, the tank will be fullin:
A.6 hours B.62hours
3C.7 hours D.71hours
Pipes and Cisterns, Page 25
2
Answer: Option C
Explanation:
(A + B)'s 1 hour's work =1
+1
=9
=3
.12 15 60 20
(A + C)'s hour's work =1
+1
=8
=2
.12 20 60 15
Part filled in 2 hrs =3
+2
=17
.20 15 60
Part filled in 6 hrs = 3 x17
=17
.60 20
Remaining part = 1 -17
=3
.20 20
Now, it is the turn of A and B and3
part is filled by A and B in 1 hour.20
Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.
22. 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 ofhours taken by C alone to fill the tank is:A.10 B.12C.14 D.16
Answer: Option C
Explanation:
Part filled in 2 hours =2=
16 3
Remaining part = 1 -1
=2.
3 3
(A + B)'s 7 hour's work =23
(A + B)'s 1 hour's work = 2
Pipes and Cisterns, Page 26
21
C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }
=1-
2=
16 21 14
C alone can fill the tank in 14 hours.
Directions to Solve
Each of the questions given below consists of a question followed by three statements. You have to study thequestion and the statements and decide which of the statement(s) is/are necessary to answer the question.23. If both the pipes are opened, how many hours will be taken to fill the tank?
I. The capacity of the tank is 400 litres.II. The pipe A fills the tank in 4 hours.
III. The pipe B fills the tank in 6 hours.A.Only I and IIB.Only II and IIIC.All I, II and IIID.Any two of the threeE.Even with all the three statements, answer cannot be given.
Answer: Option B
Explanation:
II. Part of the tank filled by A in 1 hour =14
III. Part of the tank filled by B in 1 hour =16
(A + B)'s 1 hour's work =1+
1=
54 6 12
A and B will fill the tank in12
hrs = 2 hrs 24 min.5
So, II and III are needed.
Correct answer is (B).
Directions to Solve
Pipes and Cisterns, Page 27
Each of the questions given below consists of a statement and / or a question and two statements numbered Iand II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient toanswer the given question. Read the both statements and
Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data inStatement II alone are not sufficient to answer the question.
Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data inStatement I alone are not sufficient to answer the question.
Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer thequestion.
Give answer (D) if the data even in both Statements I and II together are not sufficient to answer thequestion.
Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
24. How much time will the leak take to empty the full cistern?I. The cistern is normally filled in 9 hours.
II. It takes one hour more than the usual time to fill the cistern because of la leak in the bottom.A.I alone sufficient while II alone not sufficient to answerB.II alone sufficient while I alone not sufficient to answerC.Either I or II alone sufficient to answerD.Both I and II are not sufficient to answerE.Both I and II are necessary to answer
Answer: Option E
Explanation:
I. Time taken to fill the cistern without leak = 9 hours.
Part of cistern filled without leak in 1 hour =19
II. Time taken to fill the cistern in presence of leak = 10 hours.
Net filling in 1 hour =110
Work done by leak in 1 hour =1-
1=
19 10 90
Leak will empty the full cistern in 90 hours.
Clearly, both I and II are necessary to answer the question.
Correct answer is (E).
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25. How long will it take to empty the tank if both the inlet pipe A and the outlet pipe Bare opened simultaneously?
I. A can fill the tank in 16 minutes.II. B can empty the full tank in 8 minutes.
A.I alone sufficient while II alone not sufficient to answerB.II alone sufficient while I alone not sufficient to answerC.Either I or II alone sufficient to answerD.Both I and II are not sufficient to answerE.Both I and II are necessary to answer
Answer: Option E
Explanation:
I. A's 1 minute's filling work =116
II. B's 1 minute's filling work =18
(A + B)'s 1 minute's emptying work =1-
1=
18 16 16
Tank will be emptied in 16 minutes.
Thus, both I and II are necessary to answer the question.
Correct answer is (E).
Pipes and Cisterns, Page 29
PROBLEMS FOR THE TEST
1.Two taps A and B can fill a tank in 10 hours and 15 hours and 15 hours respectively. Ifboth the taps are opened together, the tank will be full in ?
Ans:6hrs2.To fill a cistern, pipes A,B and C take 20 minutes, 15 minute and 12 minutes resp. Thetime in minutes that the three pipes together will take to fill the cistern is
Ans:53.Two pipes can fill a tank in 10 hours and 12 hours resp. while third pipe empties thefull tank in 20 hours. If all the three pipes operate simultaneously, in how much time thetank will be filled?
Ans;7 hrs 30 mins4.A cistern can be filled in 9 hours but it takes 10 hours due to a leak in its bottom. If thecistern is full, then the time that the leak will take to empty it is
Ans:90 hrs5.an electric pump can fill a tank in 3 horus. Because of a leak in the tank, it took 3 ½hours to fill the tank. The leak can drain out of all the water of the tank in
Ans:21 hrs6.Taps A and B can fill a bucket in 12 minutes and 15 minutes resp. If both are openedand A is closed after 3 minutes. How much further time would it take for B to fill thebucket?
Ans 8 min 15 sec7.A tank can be filled by a tap in 20 minutes and by another rtap in 60 mintues. Both tapsare kept open for 10 mintues and then the first tap is shut off. After this, the tank will becompletely filled in
Ans:20 min8.If two pipes function simultaneously the reservoir will be filled in 12 hours, one pipefills the reservoir 10 hours faster than the other. How many hours it takes the second pipeto fill the reservoir?
Ans:30 hours9.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: 6hours10.12 buckets of water fill a taken when the capacity of each bucked is 13.5 liter. Howmany buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?
Ans:1811.Bucket p has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill theempty drum. How many turns it will take for both the buckets p and q having each turntogether to fill the empty drum
ans:45
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12.Two pipes A and B fill a tank in 15 hours and 20 hours respectively while a third pipec can empty the full tank in 25 hours. All the three pipes are opened in the beginning,after 10 horus, c is closed. In how much time, will the tank be full ?
ans:12 hrs13.Two pipes A and B and can fill a cistern in 12 minutes and 15 minutes respt but athird pipe c can empty the full tank in 6 mintues. A and B are kept open for 5 minutes inthe beginning and then c is also opened. In what time is the cistern emptied …..
Ans:45 mints14.Three pipes A,B and C can fill a tank in 6 hours. After working at it together for2hours, C is closed and A and B can fill the remaining part in 7 hours. The number ofhours taken by C alone to fill the cistern is
ans:1415.A leak in the bottom of atank can empty the full tank in 8 hours. An inlet pipe fillswater are the rate of 6 literes a minute. When the tank is full, the inlet is opened and dueto the leak, the tank is empty in 12 hours. How many litres does the cistern hold ?
Ans: 8,64016.A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fillswater at the rate of 4 liters a minute. When the tank is full the inlet is opened and due tothe leak the tank is empty in 8 hours. The capacity of the tank (in litters is :
Ans 5760.17.A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank isalready half-full and both tansk are opened together, the tank will be :
ans:emptied in 8 min18.A cistern has two taps which fill it in 12 min and 15 min resp. There is also a wastepipe in the cistern. When all the three are opened, the empty cistern is full in 20 minutes.How long will waste pipe take to empty the full cistern ?
Ans;10 min19.Two pipes A and B can fill a cistern in 12 minutes and 15 mint resp. If both the pipesare opened together, then after how much time B should be closed so that the tank is fullin 9 minutes?
Ans 4 min20.Two pipes A and B can fill a tank in 6 hours and 4 hours resp. If they are opened onalternate hours and if pipe A is opened first, in how many hours, the tank shall be full ?
Ans: 5 hours
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