3rdpipes and cisterns_new1

SREENIVASA INSTITUTE OF TECHNOLOGY AND
MANAGEMENT STUDIES
Murukambattu Post, Chittoor – 517 127 (A.P)
AFFILIATED TO JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY –
ANANTAPUR,

Course material
For
Reasoning and Quantitative Aptitude

Module Name: PIPES AND CISTERNS

Page 1

PREREQUISITES:

1. Inlet:

A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an
inlet.

Outlet:

A pipe connected with a tank or cistern or reservoir, emptying it, is known as an
outlet.

2. If a pipe can fill a tank in x hours, then:

1
part filled in 1 hour = .
x

3. If a pipe can empty a tank in y hours, then:

1
part emptied in 1 hour = .
y

4. 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, then

11
the net part filled in 1 hour = - .
xy

5. 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, 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)

Page 2

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 empty the
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' can empty the
full tank in 'e'hrs.If the tank is full & all the three pipes are opened simultaneously . 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 the bottom.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)

Page 3

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
xy
A and B together will do the work in hours
x y

Answer with Explanation:

Time taken by A = 10 hours

Time taken by B = 15 hours

15 X 10
Time taken by A and B =
15 10

15X 10
= = 6 hours.
25

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 TCS 2008

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

Page 4


1 minutes work of each of the three pipes

= 1/20 + 1/15 + 1/12

3 4 5 12
= =
60 60

= 1/5

= 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


1 minutes work of each of the three pipes

= 1/10 + 1/12 - 1/20

6 5 3 8
= =
60 60

2
=
15

= 15/2 hours = 7 ½ hour

= 7 hours 30 minutes.

Page 5

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: CAT 2007
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
xy
filled (empty) in hours
x y


Time taken by A = 9 hours

Time taken by B = 10 hours

9 x10
Time taken by A and B =
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: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
xy
(empty) in hours
x y


Time taken = 3 hours

Time taken = 3 ½ hours

1
3 x3
Time taken by A and B = 2
1
3 3
2

Page 6

7
3x
= 2
7
3
2

7
3x
= 2
7 6
2

= 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? WIPRO 2009
Ans 8 min 15 sec

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.


For 3 minutes (I part)

1 1
=3
12 15

15 12
= 3
15 X 12

3
= 3 = 9/20
20

Remaining part

= 1- 9/20 = 11/20

Page 7

Tap B fill the bucket in

11
= -15
20

= 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


For 10 minutes (I part)

1 1
= 10
20 60

4
= 10
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

Page 8
= 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? ACCENTURE 2008
Ans:30 hours

Basic Formula:

xy
Taken unknown value as x and use
x y


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

x 10 x
= 1/12
x( x 10)

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.

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

Page 9

Basic Formula:

Pipe A can fill a tank in ‘x’ hours and pipe B can empty it in ‘y’ hours. If both the pipes
xy
opened together, the tank will be filled in hours.
x y


Time taken to fill the tank = 2 hours

Time taken to empty the tank = 3 hours

2X 3
Time taken to fill the cistern =
3 1

= 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 CTS 2007

Basic Formula:

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 = 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

12X 13.5
= N2 = = 54/3
9

Page 10
= 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:

xy
x y


Bucket P has thrice the capacity as bucket Q

Q= 3 P

P takes 60 turns

Q takes = 180 turns

180 X 60
P and Q takes =
60 180

180X 60
=
240

= 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


A B C

Page 11
15 20 -25

1 1 1
For 10 hours = 10
15 20 25

20 15 12
= 10
300 300 300

23
= 10
300

= 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


A B C

12 15 -6

1 1
For 5 minutes = 5
12 15

Page 12

27
= 5
180

= 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.

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: INFOSYS 2008
Answer:14

Basic Formula:

C’s work = (A+B+C)’s work – (A+B)’s work


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

Page 13

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


Time taken to fill the tank is 1/8

Time taken to empty the taken is 1/12

1 1 12 8
Work done by the inlet in 1 hour = =
8 12 12 X 8

4
= = 1/24
12 X 8

Work done by the inlet in 1 minute = 1/24 X 1/60 = 1/1440

Therefore Volume = 1440 X6 liters

= 8640 liters

Page 14

Solved 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. CAT 2010

Basic Formula:


Time X number of liters


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)

8 6
= = 2 / 48 = 1/24
6X 8

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:



Time taken to fill the tank in = 1/16 min

Page 15
Time taken to empty the tank in = 1/8 min

Work done by both in 1 min = (1/16 – 1/8)

8 16
= = -8 / 16X8
16 X 8

= -1/16 (-ve means empty)

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


27
To fill the cistern = (1/12 + 1/15) =
12 X 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.

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? CAT 2010

Page 16
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

1 1
x + (9-x) X 1/12 = 1
12 16
16 12 9 x
x = 1
12 X 16 12 12
28
x - x/12 = 1-9/12
12 x16

7x x
= 3/12
12 x 4 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


Water level in the tank is 2/5

Page 17

10 6 4 1
Both the pipes are open = = =
10 X 6 60 15

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


A = 20

B = 30

Together = A+B/AB

20 30
=
20 X 30

50 1
= =
20 X 30 12

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


A = 36

B = 45

Page 18

AB 36 X 45
=
A B 36 45

36X 45
=
81

= 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 ? INFOSYS 2007

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


1 1 4 6
(A+B)’s 2 hours work when opened alternately = =
6 4 24

(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

Page 19

9.A tank is fitted with 8 pipes, some of them that fill the tank and others that are waste pipe

meant to empty the tank. Each of the pipes that fill the tank can fill it in 8 hours, while each

of those that empty the tank can empty it in 6 hours. If all the pipes are kept open when the

tank is full, it will take exactly 6 hours for the tank to empty. How many of these are fill

pipes?
(1) 2 (2) 4 (3) 6 (4) 5
Correct Answer - (2)

Solution:

Let the number of fill pipes be ‘n'. Therefore, there will be 8-n, waste pipes.
Each of the fill pipes can fill the tank in 8 hours. Therefore, each of the fill pipes will fill 1/8th
of the tank in an hour.
Hence, n fill pipes will fill n/8th of the tank in an hour.

Similarly, each of the waste pipes will drain the full tank in 6 hours. That is, each of the waste
pipes will drain 1/6th of the tank in an hour.
Therefore, (8-n) waste pipes will drain ((8-n)/6)th of the tank in an hour.

Between the fill pipes and the waste pipes, they drain the tank in 6 hours. That is, when all 8
of them are opened, 1/6th of the tank gets drained in an hour.

(Amount of water filled by fill pipes in 1 hour - Amount of water drained by waste pipes 1
hour)
= 1/6th capacity of the tank drained in 1 hour.

n/8 - 8-n / 6 = -1/6 => 6n-64+8n / 48 = -1/6 => 14n-64= -8 or 14n = 56 or n=4

Note: In problems pertaining to Pipes and Cisterns, as a general rule find out the amount of
the tank that gets filled or drained by each of the pipes in unit time (say in 1 minute or 1
hour).

10.There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others

are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes

can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an

empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?
(1) 6 (2) 8 (3) 7 (4) 5

Page 20

ANS:3

Solution

Let there be ‘n’ fill pipes attached to the tank.
Therefore, there will be 12 - n drain pipes attached to the tank

Each fill pipe fills the tank in 8 hours. Therefore, each of the fill pipes will fill 1/8th of the
tank in an hour.
Hence, n fill pipes will fill n*1/8 = n/8 th of the tank in an hour.
Each drain pipe will drain the tank in 6 hours. Therefore, each of the drain pipes will drain
1/6 th of the tank in an hour.
Hence, 12 - n drain pipes will drain(12-n) / 6 = 12-n / of the tank in an hour.
When all these 12 pipes are kept open, it takes 24 hours for an empty tank to overflow.
Therefore, in an hour 1/24 thof the tank gets filled.
Hence,n/8 - 12 - n/6 = 1/24.
i.e.3n - 4(12-n) / 24 = 1/24 or 7n - 48 = 1 => 7n = 49 or n = 7.

11.A pump can be used either to fill or to empty a tank. The capacity of the tank is 3600 m3.

The emptying capacity of the pump is 10 m3/min higher than its filling capacity. What is the

emptying capacity of the pump if the pump needs 12 more minutes to fill the tank than to

empty it?

(1) 50 m3 / min (2) 60 m3 / min (3) 45 m3 / min (4) 90 m3 /min


Solution:

Let ‘f’ m3/min be the filling capacity of the pump. Therefore, the emptying capacity of the

pump will be= (f + 10) m3 / min.

The time taken to fill the tank will be = 3600 / f minutes

And the time taken to empty the tank will be = 3600 / f+10.

We know that it takes 12 more minutes to fill the tank than to empty it

i.e 3600/f - 3600 / f+10 = 12 => 3600 f + 36000 - 3600 f = 12 (f2 + 10 f)

Page 21

=> 36000 = 12 (f2 + 10 f) => 3000 = f2 + 10 f => f2 + 10 f - 3000 = 0.

Solving for positive value of ‘f’ we get, f = 50.

Therefore, the emptying capacity of the pump = 50 + 10 = 60 m3 / min

12.Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it

takes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tank

if pipe A is shut?

(1) 2 hours 30 minutes (2) 5 hours (3) 4 hours (4) 10 hours


Solution:

Pipe A fills the tank normally in 2 hours. Therefore, it will fill ½ of the tank in an hour.

Let the leak take x hours to empty a full tank when pipe A is shut. Therefore, the leak will

empty 1/4 of the tank in an hour.

The net amount of water that gets filled in the tank in an hour when pipe A is open and when

there is a leak = 1/2 -1/x of the tank. — (1)

When there is a leak, the problem states that Pipe A takes two and a half hours to fill the tank.

i.e. 5/2 hours. Therefore, in an hour, 5/2 th of the tank gets filled. – (2)

Equating (1) and (2), we get 1/2 - 1/x =2/5=> 1/x = 1/2 - 2/5 = 1/10 => x = 10 hours.

13. There are 12 pipes attached to a tank. Some of them are fill pipes and some are drain

pipes. Each of the fill pipes can fill the tank in 12 hours, while each of the drain pipes will

take 24 hours to drain a full tank completely. If all the pipes are kept open when the tank was

empty, it takes 2 hours for the tank to overflow. How many of these pipes are drain pipes?

(1) 6 (2) 11 (3) 4 (4) 7


Page 22

There are 12 pipes attached to the tank. Let ‘n’ of them be fill pipes. Therefore, there will be

12-n drain pipes.

Each fill pipe, fills the tank in 12 hours. Therefore, 1/12th of the tank gets filled every hour

by one fill pipe.

‘n’ fill pipes will, therefore, fill n/12 th of the tank in an hour.

Each drain pipe drains the tank in 24 hours. That is, 1/24 th of the tank gets drained by one

drain pipe every hour.

12-n drain pipes, will therefore, drain 12-n / 24 th of the tank in an hour.

When all the pipes are open when the tank is empty, it takes 2 hours for the tank to overflow.

i.e. ½ the tank gets filled every hour.

Equating the information, we get n/12 - 12-n/24 = 1/2

=> 2n+n-12 / 24 = 1/2 => 3n - 12 = 12 or 3n = 24 or n = 8.

Therefore, there are 8 fill pipes and (12 - 8) = 4 drain pipes.

14.Pipe A can fill a tank in 'a' hours. On account of a leak at the bottom of the tank it takes

thrice as long to fill the tank. How long will the leak at the bottom of the tank take to empty a

full tank, when pipe A is kept closed? CAT 2010

(1) (3/2)a hours (2) (2/3)a (3) (4/3)a (4) (3/4)a


Solution:

Pipe A fills the tank in 'a' hours. Therefore, of the tank gets filled in an hour. On account of

the leak it takes 3a hours to fill the tank. Therefore, of the tank gets filled in an hour. Let the

leak at the bottom of the tank take 'x' hours to empty the tank. Hence, 1/x of the tank gets

emptied every hour.

1/a - 1/x =1/3a => 1/x =1/a - 1/3a = 2/3a

Page 23
Hence, x = 3a/2

15.Pipe A fills a tank in 30 minutes. Pipe B can fill the same tank 5 times as fast as pipe A. If
both the pipes were kept open when the tank is empty, how much time will it take for the tank
to overflow?

Explanatory Answer
Pipe B fills the tank 5 times as fast as pipe A.
Therefore, pipe B will fill the tank in one-fifth of the time that pipe A takes.

Pipe B will fill the tank in = 6 minutes.

In 1 minute, pipe A will fill th of the tank and pipe B will fill th of the tank.

Therefore, together, the two pipes will fill th of the tank in a minute
Hence, the two pipes working together will take 5 minutes to fill the tank.

16.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 proportion of the solution R

in the liquid in the tank after 3 minutes?

5 6
A. B.
11 11

7 8
C. D.
11 11

Answer: Option B

Explanation:

1 1 1 11 11
Part filled by (A + B + C) in 3 minutes = 3 + + = 3x = .
30 20 10 60 20

.

Page 24

Part filled by C in 3 minutes = 3

10

3 20 6
Required ratio = x = .
10 11 11

17. Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can
empty it in 12 hours. If all the three pipes are opened together, then the tank
will be filled in:
13 8
A. 1 hours B.2 hours
17 11

9 1
C. 3 hours D.4 hours
17 2

Answer: Option C

Explanation:

1 1 1 17
Net part filled in 1 hour + - = .
5 6 12 60

60 9
The tank will be full in hours i.e., 3 hours.
17 17

18.A pump can fill a tank with water in 2 hours. Because of la leak, it took 2 hours to fill
the tank. The leak can drain all the water of the tank in:

1
A. 4 hours B.7 hours
3

C. 8 hours D.14 hours

Answer: Option D

Explanation:

13 1
Work done by the leak in 1 hour = - = .
2 7 14

Page 25

Leak will empty the tank in 14 hrs.

19.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 turned off 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.

2 1 2
x + + (30 - x). = 1
75 45 75

11x (60 -2x)
+ =1
225 75

11x + 180 - 6x = 225.

x = 9.

20.A tank is filled by three pipes with uniform flow. The first two pipes operating
simultaneously fill the tank in the same time during which the tank is filled by the third pipe
alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than
the third pipe. The time required by the first pipe is:

A.6 hours B.10 hours

C.15 hours D.30 hours

Answer: Option C

Explanation:

Suppose, first pipe alone takes x hours to fill the tank .

Page 26

Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank.

1 1 1
+ =
x (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]

21.Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3
gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The
capacity of the tank is:

A.60 gallons B.100 gallons

C.120 gallons D.180 gallons

Answer: Option C

Explanation:

1 1 1
Work done by the waste pipe in 1 minute = - +
15 20 24

1 11
= -
15 120

1
=- . [-ve sign means emptying]
40

1
Volume of part = 3 gallons.
40

Page 27
Volume of whole = (3 x 40) gallons = 120 gallons.

22.A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and
B is twice as fast as A. How much time will pipe A alone take to fill the tank?
A.20 hours B.25 hours

C.35 hours D.Cannot be determined

E. None of these

Answer: Option C

Explanation:

Suppose pipe A alone takes x hours to fill the tank.

x x
Then, pipes B and C will take and hours respectively to fill the tank.
2 4

1 2 4 1
+ + =
x x x 5

7 1
=
x 5

x = 35 hrs.

23.Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately,
then B would have taken 6 hours more than A to fill the cistern. How much time will be taken
by A to fill the cistern separately?

A.1 hour B.2 hours

C.6 hours D.8 hours

Answer: Option C

Explanation:

Let the cistern be filled by pipe A alone in x hours.

Then, pipe B will fill it in (x + 6) hours.

1+ 1 =1

Page 28

x (x + 6) 4

x+6+x 1
=
x(x + 6) 4

x2 - 2x - 24 = 0

(x -6)(x + 4) = 0

x = 6. [neglecting the negative value of x]

24. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are
used together, then how long will it take to fill the tank?

A.12 min B.15 min

C.25 min D.50 min

Answer: Option A

Explanation:

1
Part filled by A in 1 min = .
20

1
Part filled by B in 1 min = .
30

1 1 1
Part filled by (A + B) in 1 min = + = .
20 30 12

Both pipes can fill the tank in 12 minutes.

25.. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the
pipes are opened together but after 4 minutes, pipe A is turned off. What is the total
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.

Page 29

Answer: Option D

Explanation:

1 1 7
Part filled in 4 minutes = 4 + = .
15 20 15

7 8
Remaining part = 1 - = .
15 15

1
Part filled by B in 1 minute =
20

1 8
: :: 1 : x
20 15

8 2
x= x 1 x 20 = 10 min = 10 min. 40 sec.
15 3

The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.

26. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can
fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
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.

x
Then, faster pipe will fill it in minutes.
3

1 3 1

+ =
x x 36

Page 30

4 1
=
x 36

x = 144 min.

27. A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes
respectively. How many minutes will it take to fill the tanker from empty state if B is
used for half the time and A and B fill it together for the other half?
A. 15 min B.20 min

C. 27.5 min D.30 min

Answer: Option D

Explanation:

1 1 1
Part filled by (A + B) in 1 minute = + = .
60 40 24

Suppose the tank is filled in x minutes.

x 1 1
Then, + =1
2 24 40

x 1
x =1
2 15

x = 30 min.

28. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are
opened. What is the total time taken to fill the tank completely?
A.3 hrs 15 min B.3 hrs 45 min

C.4 hrs D.4 hrs 15 min

Answer: Option B

Explanation:

Time taken by one tap to fill half of the tank = 3 hrs.

Page 31

1 2
Part filled by the four taps in 1 hour = 4 x = .
6 3

1 1
2 2

21
: :: 1 : x
32

1 3 3
x= x 1 x = hours i.e., 45 mins.
2 2 4

So, total time taken = 3 hrs. 45 mins.

29. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open
all the time and B and C are open for one hour each alternately, the tank will be full in:
2
A.6 hours B.6 hours
3

1
C.7 hours D.7 hours
2

Answer: Option C

Explanation:

1
1 9 3
(A + B)'s 1 hour's work = + = = .
12 15 60 20

1 1 8 2
(A + C)'s hour's work = + = = .
12 20 60 15

3 2 17
Part filled in 2 hrs = + = .
20 15 60

Page 32

17 17
Part filled in 6 hrs = 3 x = .
60 20

17 3
20 20

3
Now, it is the turn of A and B and part is filled by A and B in 1 hour.
20

Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.

30. 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 tank is:
A. 10 B.12

C. 14 D.16

Answer: Option C

Explanation:

2 1
Part filled in 2 hours = =
6 3

1 2
3 3

2
(A + B)'s 7 hour's work =
3

2
(A + B)'s 1 hour's work =
21

C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }

1 2 1
= - =
6 21 14

Page 33

C alone can fill the tank in 14 hours.

31. 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 II

B. Only II and III

C. All I, II and III

D. Any two of the three

E. Even with all the three statements, answer cannot be given.

Answer: Option B

Explanation:

1
II. Part of the tank filled by A in 1 hour =
4

1
III. Part of the tank filled by B in 1 hour =
6

1 1 5
(A + B)'s 1 hour's work = + =
4 6 12

12
A and B will fill the tank in hrs = 2 hrs 24 min.
5

So, II and III are needed.

Correct answer is (B).

32. 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 answer

B. II alone sufficient while I alone not sufficient to answer

Page 34

C. Either I or II alone sufficient to answer

D. Both I and II are not sufficient to answer

E. Both I and II are necessary to answer

Answer: Option E

Explanation:

I. Time taken to fill the cistern without leak = 9 hours.

1
Part of cistern filled without leak in 1 hour =
9

II. Time taken to fill the cistern in presence of leak = 10 hours.

1
Net filling in 1 hour =
10

1 1 1
Work done by leak in 1 hour = - =
9 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).

33.How long will it take to empty the tank if both the inlet pipe A and the outlet pipe B are
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 answer
B.II alone sufficient while I alone not sufficient to answer
C.Either I or II alone sufficient to answer
D.Both I and II are not sufficient to answer
E.Both I and II are necessary to answer

Answer: Option E

Explanation:

Page 35

1
I. A's 1 minute's filling work =
16

1
II. B's 1 minute's filling work =
8

1 1 1
(A + B)'s 1 minute's emptying work = - =
8 16 16

Tank will be emptied in 16 minutes.

Thus, both I and II are necessary to answer the question.

Correct answer is (E).

34.Pipe A fills a tank of 700 litres capacity at the rate of 40 litres a minute. Another pipe B
fills the same tank at the rate of 30 litres a minute. A pipe at the bottom of the tank drains the
tank at the rate of 20 litres a minute. If pipe A is kept open for a minute and then closed and
pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute
and then closed and the cycle repeated, how long will it take for the empty tank to overflow?
(1) 42 minutes
(2) 14 minutes
(3) 39 minutes
(4) 40 minutes 33 seconds
(5) None of these

Correct Choice - (5). Correct Answer is None of these
Explanatory Answer

Pipe A fills the tank at the rate of 40 litres a minute. Pipe B at the rate of 30 litres a minute
and Pipe C drains the tank at the rate of 20 litres a minute.
If each of them is kept open for a minute in the order A-B-C, the tank will have 50 litres of
water at the end of 3 minutes.
After 13 such cycles, the tank will have 13 * 50 = 650 litres of water.
It will take 13 * 3 = 39 minutes for the 13 cycles to be over.
At the end of the 39th minute, Pipe C will be closed and Pipe A will be opened. It will add 40
litres to the tank.
Therefore, at the end of the 40th minute, the tank will have 650 + 40 = 690 litres of water.
At the end of the 40th minute, Pipe A will be closed and Pipe B will be opened. It will add 30
litres of water in a minute.
Therefore, at the end of the 41st minute, the tank will have 690 + 30 = 720 litres of water.
But then at 700 litres, the tank will overflow. Therefore, Pipe B need not be kept open for a
full minute at the end of 40 minutes.

Page 36
Pipe B needs to add 10 more litres of water at the end of 40 minutes. It will take 1/3rd of a

minute to fill 10 litres of water.
Therefore, the total time taken for the tank to overflow = 40 minutes + 1/3 of a minute
or 40 minutes 20 seconds.

35.A pump can be used either to fill or to empty a tank. The capacity of the tank is 3600 m3.
The emptying capacity of the pump is 10 m3/min higher than its filling capacity. What is the
emptying capacity of the pump if the pump needs 12 more minutes to fill the tank than to
empty it?

1. 50 m3 / min
2. 60 m3 / min
3. 45 m3 / min
4. 90 m3 /min
5. 72 m3 /min

Correct Choice - (2). Correct Answer is 60 m3 / min

Explanatory Answer
Let 'f' m3/min be the filling capacity of the pump.
Therefore, the emptying capacity of the pump will be = (f + 10 ) m3 / min.

The time taken to fill the tank will be = minutes

And the time taken to empty the tank will be = .
We know that it takes 12 more minutes to fill the tank than to empty it

i.e = 12

=> 3600 f + 36000 - 3600 f = 12 (f2 + 10 f)

=> 36000 = 12 (f2 + 10 f) => 3000 = f2 + 10 f => f2 + 10 f - 3000 = 0.

Solving for positive value of 'f' we get, f = 50.

Therefore, the emptying capacity of the pump = 50 + 10 = 60 m3 / min

Page 37

36.There are three taps A, B and C in a container. Tap A and B can fill the container in 15
and 10 minutes respectively, if they are working alone. Tap C can empty it in 12 minutes if
it is working alone. Initially all the Taps are closed. Tap A is opened alone for 3 minutes.
Now A is closed and B is opened alone for 2 minutes. Now B is closed and C is opened
alone for 5 minutes. Finally all the three taps are opened together. How long will it take to
fill the tank?

 10 minutes

 12 minutes

 Tank Cannot be filled

 None of these

Answer :12 minutes

Solution (Fast Approach)

Part 1

 Tap A alone can fill 100% of the container in 15 min.
Its opened for 3 minutes. Hence it fills (3/15)x100 = 20% of the conatainer

 In the same way in 2 minute B can fill (2/10)x100 = 20%.

 Now container is 40% full

 Now Tap C is opened for 5 min. It can empty (5/12)x100 = 41.67% of the container in 5
min. Only 40% of the container is filled, hence C will completely empty the container.
Part 2

 In 1 min A, B and C combined can fill (1/15 + 1/10 - 1/12) = 1/12 portion of the container

 Hence 1 portion (Full) can be filled in 1/(1/12) = 12 minutes

37. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes
are opened simultaneously, how much time will be taken to fill the tank?

Sol. Part filled by A In 1 hour = 1/36
Part filled by B in 1 hour = 1/45
Part filled by (A + B) In 1 hour = [1/36 + 1/45] = 9/180 = 1/20
Hence, both the pipes together will fill the tank in 20 hours.

38. A pipe can fill a tank in 16 hours. Due to a leak in the bottom,it is filled in 24 hours. If the
tank is full, how much time will the leak take to empty it ?

Page 38

Sol. Work done by the leak in 1 hour = [ 1/16 – 1/24 ]=1/48
:. Leak will empty the full cistern in '48 hours.

39. A cistern is filled by pipe A in 10 hours and the full cistern can be leaked out by an
exhaust pipe B in 12 hours. If both the pipes are opened, in what time the cistern is full?
Sol. Work done by the inlet in 1 hour: = 1/10
Work done by the outlet in 1 hour = 1/12
Net part filled in 1 hour = [ 1/10 – 1/12 ] = 1/60
The cistern will be full in 60 hours.

40. Two pipes can fill a cistern in 14 hours and 16 hours respectively. The pipes are opened
simultaneously and it is found that due to leakage in the bottom, 32 minutes extra are taken
for the cistern to be filled up. When the cistern is full in what time will the leak empty it ?
Sol. Work done by .the two pipes in 1 hour = [ 1/14 + 1/16 ] = 15/112
... Time taken by these pipes to fill the tank = 112/15 hours
= (7 hrs. 28 min.)
Due to leakage, time taken = (7 hrs 28 min.) + 32 min. = 8 hrs
Work done by ( two pipes + leak) in 1 hour = 1/8
Work done by the leak m 1 hour = [ 15/112 – 1/8 ] = 1/112
Leak will empty the full cistern in 112 hours

41. Pipes A and B can fill a tank in 20 hours and 30 hours respectively 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 ?

Sol. Net part filled m 1 hour = [1/20 + 1/30 – 1 /40] = 7/120
The tank will be full in 120/7 = 17 ½

42. Two pipes A and B can frll a tank in 24 min. and 32 min. respectively. If both the pipes
are opened simultaneously, after how much time B should be closed so that the tank is full in
18 minutes?

Sol. Let B be closed after x minutes. Then,
part filled by (A + B) in x min. + part filled by A in (18 - x) min. = 1.
X {1/24 + 1/32] + (18 – x) X 1/24 = 1 or 7x/96 + (18 – x)/24 = 1
7x + 4(18 –x) = 96 or x=8
Hence, B must be closed after 8 minutes

43. Two pipes A and B can fill a tank in 36 min. and 4S min. respectively. A water pipe C
can empty the tank in 30 min. First A and B are opened. After 7 minutes, C is opened. In how
much time, the tank Is full ?

Sol. Part filled in 7 min = 7[ 1/36 + 1/45] = 7/20

Page 39

Remaining part = [ 1- 7/20] = 13/20

Net part filled in 1 min. When A,B and C are opened

= [ 1/36 + 1/45 + 1/30 ] = 1/60
Now, 1/60 part is filled in 1 min.

13/20 part is filled in [60x13/20] = 39 min
Total time taken to fill the tank = (39 + 7) min. = 46 min.

44.There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others
are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes
can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an
empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?

(1) 6
(2) 8
(3) 7
(4) 5
(5) 4

Correct Choice - (3). Correct Answer is 7 pipes

Explanatory Answer

Let there be 'n' fill pipes attached to the tank.

Therefore, there will be 12 - n drain pipes attached to the tank

Each fill pipe fills the tank in 8 hours. Therefore, each of the fill pipes will fill th of
the tank in an hour.

Hence, n fill pipes will fill of the tank in an hour.

Each drain pipe will drain the tank in 6 hours. Therefore, each of the drain pipes will

drain th of the tank in an hour.

Page 40

Hence, (12 - n) drain pipes will drain th of the tank in an hour.

When all these 12 pipes are kept open, it takes 24 hours for an empty tank to

overflow. Therefore, in an hour th of the tank gets filled.

Hence, .

i.e. or 7n - 48 = 1 => 7n = 49 or n = 7.

45. Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open
throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after
pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal
share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously,
the tank would be filled completely in t minutes. Find t?

A is kept open for all t minutes and fills one-third the tank. Or, A should be able to fill the
entire tank in '3t' minutes.

A and B together can fill the tank completely in t minutes. A alone can fill it in 3t minutes.
A and B together can fill 1/t of the tank in a minute. A alone can fill 1/3t of the tank in a
minute. So, in a minute, B can fill 1/t - 1/3t = 2/3t. Or, B takes 3t/2 minutes to fill an entire
tank

To fill one-third the tank, B will take t/2 minutes. B is kept open for t - 10 minutes.

t/2 = t - 10, t = 20 minutes.

A takes 60 mins to fill the entire tank, B takes 30 minutes to fill the entire tank. A is kept
open for all 20 minutes. B is kept open for 10 minutes.

C, which is kept open for 8 minutes also fills one-third the tank. Or, c alone can fill the tank
in 24 minutes.

Page 41

46.Pipe A fills a tank at the rate of 100lit/min, Pipe B fills at the rate of 25 lit/min, pipe C

drains at the rate of 50 lit/min. The three pipes are kept open for one minute each, one after

the other. If the capacity of the tank is 7000 liters, how long will it take to fill the tank if

i) A is kept open first, followed by B and then C

Each cycle of 3 minutes, 75 liters get filled. 100 + 25 - 50. So, after 3 minutes the tank would

have 75 liters

6 mins - 150 liters

9 mins - 225 liters

30 mins - 750 liters




In the 280th minute, pipe A would be open and it would fill the remaining 25 liters in 15

seconds. So, it would take 279 mins and 15 seconds to fill the tank.

The most important thing in these type of questions is to think in terms of cycles till we reach

close to the required target and then think in simple steps.

ii) B first, followed by A, and then C

Each cycle of 3 minutes, 75 liters get filled. 25 + 100 - 50. So, after 3 minutes the tank would

have 75 liters

6 mins - 150 liters

9 mins - 225 liters





In the 280th minute, pipe B would be open and it would fill the remaining 25 liters in one

minutes. So, it would take 280 mins.

Page 42

iii) B first, followed by C, and then A

In this case also, Each cycle of 3 minutes, 75 liters get filled. 25 -50 + 100. But there is a

small catch here. In the first set of 3 minutes, we would fill up to about 100 liters. After 1

minute, we would be at 25 liters, after 2 minutes, we would be at 0 liters and in the third

minute, the tank would be 100 liters full.

6 mins - 170 liters

9 mins - 250 liters





279 minutes - 7000 liters

So, it would take 279 mins and 15 seconds to fill the tank.

The mOst Important thing in these type of questions is to think in terms of cycles till we

reach close to the required target and then think in simple steps.

47. A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system

of n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, which

of the following are possible values of n (More than one option could be correct)?

1) 32 2) 54 3) 29 4) 40

3 fill pipes cancel out 2 drain pipes. Plus, you need an additional 4 fill pipes fill the tank in 5

hours. so the answer has to be 5k + 4. Both 54 and 29 are possible.

Page 43

PROBLEMS FOR THE TEST

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

2.To fill a cistern, pipes A,B and C take 20 minutes, 15 minute and 12 minutes resp. The time
in minutes that the three pipes together will take to fill the cistern is

Ans:5

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

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

5.an electric pump can fill a tank in 3 horus. 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

6.Taps A and B can fill a bucket in 12 minutes and 15 minutes resp. 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

7.A tank can be filled by a tap in 20 minutes and by another rtap 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

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

Page 44

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

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

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

ans:45

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
horus, c is closed. In how much time, will the tank be full ?

ans:12 hrs

13.Two pipes A and B and can fill a cistern in 12 minutes and 15 minutes respt 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

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

ans:14

15.A leak in the bottom of atank can empty the full tank in 8 hours. An inlet pipe fills water
are the rate of 6 literes 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

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 liters 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 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 is
already half-full and both tansk are opened together, the tank will be :

Page 45

ans:emptied in 8 min

18.A cistern has two taps which fill it in 12 min and 15 min resp. There is also a waste pipe 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 min

19.Two pipes A and B can fill a cistern in 12 minutes and 15 mint resp. 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

20.Two pipes A and B can fill a tank in 6 hours and 4 hours resp. 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

21.Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes
are open,in how many hours will the tank be filled ?

Ans:

= (1/5 + 1/6 + 1/30)
part filled by (A+B+C) in 1 hour
‹=› 1/3.
All the three pipes together will fill the tank in 3 hours.
22.A pump can fill a tank with water in 2 hours. Because of a leak, it took 2x1/3 hours to fill
the tank. The leak can drain all the water of the tank in

A. 5 hours B. 7 hours

C. 8 hours D. 14 hours

Ans:Leak will empty the tank in 14 hours

23.Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3
gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The
capacity of the tank is

A. 60 gallons B. 80 gallons

C. 120 gallons D. 160 gallons

Ans:Work done by the waste pipe in 1
minute = 1/15 - (1/20+1/24)

Page 46

= (1/15 - 11/20)
[ - ve sigh means
= - 1/40
emptying]
Volume of 1/40 part = 3 gallons.

Volume of Whole = (3×40)
=120 gallons.
24.Two pipes can fill a tank in 10 hours and 12 hours respectively while a third pipe empties the
full tank in 20 hours.If all the three pipes operate simultaneously, in how much time will the tank
be filled?

A. 7 hrs 30 min B. 7 hrs 45 min

C. 8 hrs 30 min D. 8 hrs 45 min

Net apart filled in 1 hour = (1/10+1/12-1/20)

= 8/60
= 2/15.
Therefore the tank will be full in 15/2 hours ‹=› 7 hrs 30 min.

BANK EXAM QUESTIONS

25 A cistern can be filled by pipe A and B in 12 minutes and 10 minutes respectively. The
full tank can be emptied by a third pipe C in 8 minutes only. If all the taps be turned on at the
same time, the cistern will be full in how much time?

Ans:17(1/7) Minutes
26 Two pipes A and B can fill a tank in 10 hours and 15 hours respectively. If both the pipes
open together how much time will it take to fill the tank?

Ans:6 Hours
27. Two pipes A and B can fill a tank in 60 minutes. If pipe A alone can fill it in 75 minutes.
How much time will the pipe B take to fill the tank alone?

Ans:300 Minutes
28. Three pipes A, B and C can fill a tank in 30 hours, 20 hours and 10 hours respectively. If
all the pipes open together how much time is required to make the tank full?

Ans:5 (5/11) Hours

Page 47

29. Three pipes A, B and C together can fill a tank in 15 minutes. One of the pipes can fill it
in 45 minutes and another in 30 minutes. How much time is taken by the third pipe alone to
make the tank full?

Ans:90 Minutes
30. A cistern can be filled by pipe A and B in 40 minutes and 60 minutes respectively. There
is also an outlet C. If all the taps are open together the tank is full in 2 hours. How much time
is taken by C to empty the full tank?

Ans:30 Minutes
31. A cistern can be filled by pipe A and B in 30 minutes and 45 minutes respectively. There
is also an outlet C. If all the taps are open together the tank is full in 1 hour and 15 minutes.
How much time is taken by C to empty the full tank?

Ans:23 (13/19) Minutes
32. Pipe A can fill the tank in 12 minutes and pipe B can empty it in 8 minutes. If 3/4th part of
the tank is already full and both the pipes are open together. In much time both the pipes
empty the tank?

Ans:18 Minutes
33.A pipe can fill a tank in 40 minutes. Due to the leakage in the bottom it is filled in 50
hours. If the tank is full, how much time will the leak take to empty it?

Ans:200 Minutes
34.P, Q and R are three pipes connected to a tank. P and Q together fill the tank in 4 hours. R
and Q together fill the tank in 6 hours. P and R together fill the tank in 5 hours. In how much
time will P, Q and R fill the tank together?

Ans:3(9/37) Hours
35. Two pipes A and B can fill a tank in 25 minutes and 35 minutes respectively. But a third
pipe C can empty it in 10 minutes. The first two pipes are kept open for 5 minutes in the
beginning and then the third pipe is also opened. In what time is the cistern emptied?

Ans:10(10/11) Hours
36. A cistern can be filled by pipe A and B in 25 hours and 30 hours respectively. There is
also an outlet C which can empty it in 40 hours. If all the taps are open together. After 5
minutes pipe C must be turned off. In how much time the cistern is full?

Ans:10(15/44) Hours
37. A tank has a leak which would empty it in 16 hours. A tap is turned on which admits 12
liter a minute into the tank and it is now emptied in 24 hours. How many liters does the tank
hold?

Ans:34560 Liters

Page 48

38.Two pipes A and B can fill a tank in 12 minutes and 16 minutes respectively. If both the
pipes open together after how much time should be B closed so, that the tank is full in 9
minutes?

Ans:4 Hours
39.Two pipes A and B can fill a tank in 10 hours and 12 hours respectively. B is open for 2
hours in the beginning, and then B is closed. In how much time A fill the remaining tank?

Ans:8(1/3) Hours
40.Two pipes A and B can fill a tank in 50 minutes and 60 minutes respectively. If both the
pipes open together for 10 minutes, then B is closed. In how much time A fill the remaining
tank?

Ans:38 Minutes

Page 49

25.A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water
at the rate of 6 litres 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 ?

A. 7580 B. 7960

C. 8290 D. 8640

Ans: = (1/8 - 1/12)
Work done by the inlet in 1 hour
= 1/24.
= (1/24 × 1/60)
Work done by the inlet in 1 min.
= 1/1440.
Volume of 1/1440 part = 6 litres.
= (1440×6)
Therefore, Volume of whole
‹=› 8640 litres.

Page 50

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