pipes and cisterns - vidyarthiplus

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 yxxy+ hours

Answer with Explanation:

Time taken by A = 10 hours

Time taken by B = 15 hours

Time taken by A and B =10151015

+X

=25

1015X= 6 hours.

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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


1 minutes work of each of the three pipes

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

=60

543 ++=

6012

= 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

=60

356 −+=

608

=152

= 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) in yxxy− hours


Time taken by A = 9 hours

Time taken by B = 10 hours


109−x

= 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) in yxxy− hours


Time taken = 3 hours

Time taken = 3 ½ hours


213

2133

−

x

=3

27

273

−

x

=2

67273

−

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

Find I st part and subtract it from ‘1’ , then multiply the required

section value to find the answer.


For 3 minutes (I part)

= 3

+

151

121

= 3

+

12151215X

= 3

203

= 9/20

Remaining part

= 1- 9/20 = 11/20

Tap B fill the bucket in

=2011

-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


For 10 minutes (I part)

= 10

+

601

201

= 10

604

= 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 use yxxy+


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(

10xx

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.




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 in yxxy− hours.


Time taken to fill the tank = 2 hours

Time taken to empty the tank = 3 hours

Time taken to fill the cistern =1332

−X

= 6 hours.




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


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

= N2 =9

5.1312X= 54/3

= N2 = 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:

Answer:45


Basic Formula:

= yxxy+


Bucket P has thrice the capacity as bucket Q

Q= 3 P

P takes 60 turns

Q takes = 180 turns

P and Q takes =1806060180

+X

=240

60180X

= 45 turns.




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


Basic Formula:

1/x +1/y - 1/z Part I and Part II = 1


A B C

15 20 -25

For 10 hours = 10

−+

251

201

151

= 10

−+

30012

30015

30020

= 10

30023

= 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




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


Basic Formula:

1/x +1/y - 1/z


A B C

12 15 -6

For 5 minutes = 5

+

151

121

= 5

18027

= 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.




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


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




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


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

Work done by the inlet in 1 hour =

+

121

81

=812812X−

=812

4X = 1/24

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

Therefore Volume = 1440 X6 liters

= 8640 liters




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.


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)

=8668X−

= 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




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


Basic Formula:



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

168X

−= -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.




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


Basic Formula:

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

A + B = 1/x+1/y


To fill the cistern = (1/12 + 1/15) =1512

27X

= 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.




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


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


∴

+

161

121x + (9-x) X 1/12= 1

12129

16121216 xX

x −+

+

= 1

x1612

28x - x/12 = 1-9/12

124127 xxx − = 3/12

7x – 4x = 12

3x = 12

X = 4

So, B must be closed after 4 minutes.




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


Basic Formula:

AB/B-A


Water level in the tank is 2/5

Both the pipes are open = 610610

X−

=604

=151

Therefore 2/5 X15 = 6 minutes




21. 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

=30203020

X+

=3020

50X

=121

Therefore 12 minutes.




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


Basic Formula:

Time taken to fill the tank = A+B/AB


A = 36

B = 45

BAAB

+=

45364536

+X

=81

4536X

= 20 hours




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


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


∴ (A+B)’s 2 hours work when opened alternately =

+

41

61

= 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 - vidyarthiplus

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