Pipes and Cisterns

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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.

If a pipe can fill a tank in x hours, then:part filled in 1 hour = 1 / x
If a pipe can empty a tank in y hours, then:part emptied in 1 hour = 1
If a pipe can fill a tank in y/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 filled in 1 hour = (1/x – 1/y)
If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes, then the net part emptied in 1 hour = (1/y – 1/x)

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Pipes and cisterns - Question and Answers

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Question 1

Pipe A and Pipe B can be fill a tank in 20 minutes and 30 minutes respectively. Pipe C can empty the tank in 60 minutes. The tank is initially empty. Both the pipes A and B are opened. Pipe C is opened after 6 minutes. How much time does it take to fill the tank?

A	12minutes
B	13.5 minutes
C	15minutes
D	14.5 minutes

Question 1 Explanation:

1/30th of the tank is filled by pipe B in 1 minutes
1/60th of the tank is emptied by pipe C in 1 minutes
Part of tank filled in the first 6 minutes = 6*[(1/20)+(1/30)] = ½
When all pipes are opened, part of tank filled in 1 minutes = (1/12)-(1/60) = 1/15
Time required to fill the remaining ½ of the tank = (1/2) / (1/15) = 7.5
Total time = 6+7.5 = 13.5 minutes

Question 2

Pipe A and Pipe B can fill a tank in 20 minutes and 10 minutes respectively. Pipe C can empty the tank in 15 minutes. If the three pipes are opened simultaneously, find the time taken to fill the tank/

A	12
B	15
C	20
D	18

Question 2 Explanation:

When all pipes are opened simultaneously, part of tank filled in 1minutes
= (1/20) + (1/10) – (1/15) = 1/12
Time taken to fill the tank = 12 minutes

Question 3

Pipes P and Q can empty a tank in 1 hr and 1.5 hrs respectively. Pipes R and S can fill a tank in 2 hrs and 2.5 hrs respectively. The tank is filled to its capacity of 15 litres and all four pipes are opened simultaneously. How much water remains in the tank after an hour?

A	7 liters
B	5 liters
C	3.5 liters
D	2.5 liters

Question 3 Explanation:

Part of tank emptied by P in an hour = 1
Part of tank emptied by Q in an hour = 1/1.5 = 2/3
Part of tank filled by R in an hour = ½
Part of tank filled by S in an hour = 1/ 2.5 = 2/5
Part of tank emptied in an hour = (1+ (2/3)) - (1/2 + (2/5)) = 23/30
Water remaining in the tank = 15*7/30 = 3.5 liters

Question 4

Three pipes A,B, C are attached to a tank. A and B can fill it in 20 and 30 minutes respectively while C can empty it in 15 minutes. If A,B and C are kept open successively for 1 minutes each, how soon will the tank be filled?

A	180 minutes
B	167 minutes
C	200 minutes
D	178 minutes

Question 4 Explanation:

Part of the tank filled in 3 minutes = (1/20) + (1/30) – (1/15) = 1/60
Part filled in 165 minutes = (165/3) * (1/60) = 55/60
Part filled in 167 minutes = (55/60) + (1/20) + (1/30) = 60/60 = 1
The tank is filled in 167 minutes

Question 5

Pipe A and B can fill a tank in 1 hour and1 ¼ hours respectively. Both pipes are opened in the beginning and after some time, pipe B is closed. The tank is filled in 40 minutes. Pipe B was closed after?

A	30 minutes
B	45 minutes
C	40 minutes
D	25 minutes

Question 5 Explanation:

Part of tank filled by A in a minute = 1/60
Part of tank filled by B in a minutes =1/75
Let pipe B be closed after x minutes
Part of tank filled in x minutes= x*[(1/60)+(1/75)] = 9x / 300 Part of tank filled in (40-x) minutes = [(40-x)*(1/60)] = (40-x) / 60
(9x / 300) + ((40 - x) / 60) = 1 4x = 100
X= 25

Question 6

Two pipes A and B can fill a tank in 20 min, when opened simultaneously. If pipe A alone takes 60 minutes to fill the tank, how much time will pipe B alone take to fill the tank?

A	60 minutes
B	40 minutes
C	30 minutes
D	20 minutes

Question 6 Explanation:

Let B take x minutes to fill the tank
Part of the tank filled by A and B = (1/60) + (1/x) = (1/20)
Solving this, x= 30

Question 7

A pipe can fill a tank in an hour. Because of a leak, it took 1 hour and 10 minutes to fill the tank. Find the time taken by the leak to drain all the water in the tank?

A	10 minutes
B	7/6 hours
C	6/7 hours
D	7hours

Question 7 Explanation:

Let the leak take x to drain the tank 1hr 10 min = 1+(1/6) = 7/6 hrs
1- (1/x) = 1/ (7/6) = 6/7
Part of tank leaked in an hour = 1-6/7 = 1/7
The leak takes7 hours to drain all the water

Question 8

Two taps A and B can fill a bathtub in 10 minutes and 15 minutes respectively. If A was open for the first two minutes, B for the next two minutes and so on, the bathtub is filled in ?

A	6 minutes
B	12 minutes
C	12.5 minutes
D	24 minutes

Question 8 Explanation:

Part of the tub filled in the first 2 minutes = 2*1/10 =1/5 Part of the tub filled in the next 2 minutes = 2*1/15 = 2/15
Part of the filled in 4 minutes = (1/5) +(2/15) =1/3
Time required to fill the tub = 3*4 = 12 minutes

Question 9

A tank has three inlets A,B and C. C takes twice the time taken by A to fill the tank and B takes half the time taken by A to fill the tank. If they can fill the tank together in 4 minutes, find the time taken by B to fill the tank?

A	7 minutes
B	14 minutes
C	3.5 minutes
D	28 minutes

Question 9 Explanation:

Let A take x minutes to fill the tank (1/x) + (1/ (x/2)) + (1/2x) = 1/4
(7/2x) = ¼
x=14
x /2 = 7

Question 10

An inlet pipe fills a tank at the rate of 5 liters of water a minutes. An outlet connected to the tank can empty a full tank i 5 hours. Both the piped are opened together for 30 minutes and then , the outlet is closed. It took another 36 minutes to fill the tank. Find the capacity of the tank

A	480 liters
B	360 liters
C	300 litres
D	240 liters

Question 10 Explanation:

Part of the tank filled by the inlet in a minute = (1/x)
Part of the tank emptied by the outlet in a minute = 1 / (5*60) = 1/300
Part of the tank filled in the first 30 minutes = 30*[(1/x) - (1/300)]
= (300 - x) / 10x Part of the tank filled in the next 36minutes = 36 * (1/x)
1 – [(300 - x) / 10 x] = 36 / x
Solving, x= 60
Capacity of tank = 60 * 5 = 300 liters

Question 11

Pipe A fills a tank at the rate of 5 liters every hour. Pipe B fills another tank at a rate of 1 litre in the first hour, 2litres in the second hour, 3 in the third and so on. After how many hours will the volume of water contained in the two tanks be equal?

A	10hours
B	5 hours
C	9 hours
D	6 hours

Question 11 Explanation:

Let the water contained in the tanks be equal after x hours
5x= 1+2+3+ .......+x
5x = x(x+1) / 2
X= 9 hours

Question 12

Pipe A can fill a tank thrice as faster as pipe B. If pipe A alone can fill the tank i n 20 minutes, how long does it take to fill tank if both the pipes are opened?

A	15 minutes
B	30 minutes
C	12 minutes
D	10 minutes

Question 12 Explanation:

Part of tank filled by pipe A in 1 minute= 1/20
Part of tank filled by B in 1 minute = (1/20) / 3 = 1/60
Part of tank filled by them together in 1 min = (1/20) + (1/60) = 1/15
They take 15 min to fill the tank

Question 13

A tap can fill a bucket in 10 min. Due to a leak in the bucket, it takes 12min to fill. After the tap is closed, the leak empties the bucket in?

A	20 minutes
B	1 hour
C	30 minutes
D	60 minutes

Question 13 Explanation:

Let the leak take x minutes to empty the bucket
Part of bucket filled by the tap in 1 minute =1/10
(1/10) – (1/x) = (1/12)
X = 60 minutes

Question 14

An empty drum can be filled with 18 buckets of water, if the capacity of each bucket is 16 liters. How many buckets will be need to fill the drum if the capacity of each bucket is 12 liters?

A	28
B	20
C	15
D	24

Question 14 Explanation:

Capacity of the drum = 18 * 16 = 288 liters
No. of buckets needed = 288 / 12 = 24

Question 15

Pipe A can fill a tank in 4 hours and pipe B that can fill a tank in 2 hours. Both are opened when the tank is empty. Pipe A is closed 30 minutes before the tank overflows. How long did it take for the tank to overflow?

A	100 minutes
B	75 minutes
C	90 minutes
D	80 minutes

Question 15 Explanation:

Part of tank filled by both pipes in 1 hour = (1/4) + (1/2) = ¾
Pipe A is closed before 30 minutes of overflow
Only pipe B was opened
Part of tank filled by pipe B in 30 minutes = ¼
The remaining 3/4th of the tank was filled by pipes A and B
To fill 3/4th of the tank together, 1 hour is taken
Time for overflow = 1 hours + 30 minutes = 90 minutes

Question 16

Three pipes can fill a tank in 6, 10 and 15 hours respectively. If they are opened together, how long does it take to fill the tank?

A	3 hours
B	30 hours
C	10 hours
D	33 hours

Question 16 Explanation:

Part of tank filled by the 3 pipes in 1 hour
= (1/6) +(1/10) + (1/15)
= 10/30
= 1/3
They take 3 hours

Question 17

There are 10 pipes connected to a tank, some are inlet pipes and the others are outlets. Each of the inlet pipes can fill the tank in 6 hours and each of the outlet pipes can drain the entire tank in 8 hours. If all the pipes are opened when the tank is full, the tank is drained in half a day. How many of them are outlet pipes?

A	4
B	5
C	6
D	7

Question 17 Explanation:

Let there be x inlet pipes and (10-x) outlet pipes Part of tank filled by an inlet pipe in an hour = 1/6 Part of tank drained by an outlet pipe in an hour =1/8 If all the pipes are opened, the tank is drained in half a day (12 hours)
Part of tank drained in an hour when all are open = 1/12
Part of tank drained by (10-x) outlet pipes – Part of tank filled by x inlet pipes = 1/12
[(10-x) / 8] – [x/6] = 1/12
Solving,
3(10-x)-4x = 2
30 – 7x = 2
7x=28
X=4
There are 4 inlet pipes and 6 outlet pipes

Question 18

Water flowing from a tap fills a 5 liters can inn 2 minutes. How many such cans can be filled in 1680 seconds?

A	70 cans
B	14 cans
C	28 cans
D	84 cans

Question 18 Explanation:

1680 seconds = 28 minutes
1 can is filled in 2 minutes
14 cans can be filled in 28 minutes

Question 19

Pipes A and B can fill a tank in 8 hours and 12 hours respectively. Both of them were opened simultaneously when the tank was empty. It took 6 hours to fill the tank due to a leak in the bottom. After the pipes were closed, the leak will drain the full tank in

A	12 hours
B	18 hours
C	1day
D	2 days

Question 19 Explanation:

Let the leak take x hours to empty the tank Part of tank emptied by the leak in an hour = 1/x Part of tank filled in an hour = (1/8) + (1/12) – (1-x) =(5/24) – 1/x = 1/6
1/x = (5/24) –(1/6)
= 1/24
X= 24 hours

Question 20

Pipes A fills a cistern twice as faster as pipe B. Pipe A was opened when the tank was empty and after an hour, pipe B was also Opened. Find the time taken to fill the cistern if pipe B alone can fill it in 8 hours?

A	2 hours
B	4 hours
C	4.5 hours
D	3 hours

Question 20 Explanation:

Part of tank filled by ppe B in an hour =1/8
Part of tank filled by pipe A in an hour = ¼
In the first hour, 1/4th of the tank is filled.
The remaining 3/4th of the tank is filled by A and B together
Part of tank filled by A and B in an hour = (1/4) +(1/8) = 3/8
Time taken to fill ¾ of the tank = (3/4) / (3/8) = 2 hours
The cistern is filled in 1+ 2 = 3 hours

Question 21

Pipe X can fill a tank in 5 hour. If pipe Y is also opened, the tank is filled in 3 hours. Find the time taken by pipe Y alone to fill the tank?

A	4.5 hours
B	6 hours
C	7.5 hours
D	) 7.5 hours

Question 21 Explanation:

(1/x) + (1/y) = (1/3)
(1/y) = (1/3) – (1/5)
= 2/ 15
Y takes 15/2 = 7.5 hours to fill the tank

Question 22

Water flows from a tap at the rate of 1.2 liters per minutes. If the tap is opened for 3 hours, find the amount of water collected in the tank?

A	360 liters
B	216 liters
C	180 liters
D	144 liters

Question 22 Explanation:

Amount of water collected in 180 mins
= 180 * 1.2
= 216 liters

Question 23

Pipes P and Q can fill a tank in 40 minutes and 1 hour respectively. If they are opened together, find the time taken to fill the tank?

A	1 hr 40 min
B	36 mins
C	20 mins
D	24 mins

Question 23 Explanation:

Part of tank filled P and Q in a minute =(1/40) + (1/60)
=5/120
= 1/24
It takes 24 minutes to fill the tank

Question 24

Three pipes A,B and C take 3 hours to fill a tank. If pipes A and B alone take 6 hours and 9 hours to fill he tank, find the time taken by pipe C lone to fill the tank?

A	12 hours
B	145 hours
C	18 hours
D	24 hours

Question 24 Explanation:

(1/c) = (1/3) – (1/6) – (1/9) = (1/18)

Question 25

Two pipes A and B can fill a tank in half an hour and 1(1/2)hour respectively. An outlet at the bottom of the tank can empty a full tank in 1 hour. If all the three pipes are opened, find the time taken to fill the tank?

A	1 hour
B	36 min
C	45 min
D	54 min

Question 25 Explanation:

Part of tank filled by pipe A in 1 minute = 1/30
Part of tank filled by pipe B in 1 minute = 1/90
Part of tank emptied by the outlet in 1 minute = 1/60
Part of tank filled when all the pipes are opened = part of tank filled by inlet-part of tank emptied by outlet = (1/30) + (1/90) – (1/60)
= (6+2-3) / 180
= 1/ 36
The tank is filled in 36 mins

Question 26

An outlet pipe can empty (5/7) of the cistern in half an hour. Find the time taken to empty the full cistern.

A	70mins
B	(7/5)hrs
C	21(3/7)mins
D	42 mins

Question 26 Explanation:

(5/7) of the cistern is emptied in 30 minutes
Full cistern is emptied in 30*7/5 = 42 minutes

Question 27

Tap A can fill a cistern in 1 hour and Tap B can fill it in 30 minutes. Tap A is opened first and tap B is also opened after 15 minutes. Find the time taken to fill the cistern?

A	35 mins
B	30 mins
C	25 mins
D	20 mins

Question 27 Explanation:

Part of cistern filled by A in 1minute = (1/60)
Part of cistern filled by A in 15 mins = 15/60 = ¼
Part of cistern filled by A and B in 1 minute = (1/60)+(1/30) = 1/20
¾ th of the cistern is filled by A and B
Time taken to fill ¾ of the cistern = (3/4) /(1/20) = 15 minutes
The cistern is filled in 30 minutes

Question 28

A tank is filled by two taps in half an hour. If the first tap alone takes 2 hours to fill the tank, find the time taken by the second tap alone to fill the tank?

A	40 mins
B	1 hour
C	75 mins
D	90 mins

Question 28 Explanation:

Part of tank filled by the two taps in 1 minute = 1/30
Part of tank filled by taps A in 1 minute = 1/120
(1/A) + (1/B) = (1/30)
(1/B) = (1/30) –(1/120) = (1/40)
B alone takes 40 mins to fill the tank

Question 29

A tank can be filled by 2 pipes X,Y and Z, when turned on separately, in 33 minutes, 11 minutes and 22 minutes respectively. If all are turned on for 2 mins and then Y and Z are turned off, find the time taken by X alone to fill the cistern.

A	22 minutes
B	15 minutes
C	11 minutes
D	6 minutes

Question 29 Explanation:

Part of tank filled X, Y and Z in 1 minute = (1/33) + (1/11) + (1/22) = 1/6
Part of tank filled in the first 2 minutes = 2*1/6 = 1/3
2/3 of the tank is filled by X alone
Time taken by X to fill 2/3 of the tank = (2/3) / (1/33) = 22 minutes

Question 30

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

A	20 hours
B	18 hours
C	24 hours
D	22.5 hours

Question 30 Explanation:

Part of tank filled by A in 1 hour = 1/36
Part of tank filled by B in 1 hour = 1/45
Part of tank filled by both in 1 hour = (1/36) + (1/45) = 81 / (36*45)
= 1/20
They can fill the tank in 20 hours

Question 31

15 buckets of water fill a tank when the capacity of each bucket in 12 liters. How many buckets will be needed to fill the tank in the same time, if the capacity of each bucket is 18 liters?

A	18
B	10
C	15
D	8

Question 31 Explanation:

No. of buckets needed = 15 * 12/18 = 10

Question 32

Two taps A and B can fill a tank in 5 hours and 20 hours respectively. If both the taps are open then due to a leakage, it took 30 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank?

A	18 hrs
B	36 hrs
C	35 hrs
D	9 hrs

Question 32 Explanation:

Part of tank filled by A and B in 1 hour = (1/5) + (1/20) = ¼
They take 4 hours to fill the tank. But due to the leak, they take 4.5 hours to fill the tank
Part of tank emptied by leak in 1 hours = ¼ - 1/ 4.5 = ¼ - 2/9
= 1/36
The leak can empty the tank in 36 hours

Question 33

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

A	192 mins
B	144 mins
C	108 mins
D	81 mins

Question 33 Explanation:

Let the tome taken by the faster pipe to fill tank be x mins and the time taken by the slower pipe be 3xmins
1/x + 1/3x = 1/36
4/3x = 1/36
X= 48
3x = 144

Question 34

Pipe 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, in how many hours will the tank be filled?

A	30/17
B	30/11
C	9/2
D	60/17

Question 34 Explanation:

(1/5) + (1/6) – (1/12)
= 17/60
The tank will be filled in (60/17 ) hours

Question 35

A tap can fill a tank in 6 hour. After half the tank is filled, three more similar taps are opened. What is the total time a taken to fill the tank completely?

A	4 hrs
B	3hrs 45 mins
C	4 hrs 15 mins
D	3 hrs 15 mins

Question 35 Explanation:

Half the tank is filled in 3 hours Now, 4 taps are filling the tank
Time taken by 1 tap to fill half the tank = 3
Time taken by 4 taps to fill half the tank = ¾
Total time taken = 3 hrs 45mins

Question 36

A cistern can be filled by a atap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?

A	6.5 hrs
B	4.5 hrs
C	5 hrs
D	7.2 hrs

Question 36 Explanation:

(1/4) – (1/9) = 5/36
The cistern gets filled in 36/5 = 7.2 hours

Question 37

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 alone to fill the tank is

A	10 hrs
B	15 hrs
C	30 hrs
D	6 hrs

Question 37 Explanation:

1/A + 1/B = 1/C
B = A -5
B = C + 4
C =A – 9
1/A + 1/(A-5) = 1/(A-9)
1/(A - 9) – 1/(A-5) = 1/A
Substitute the options given in the place of A
If A = 10,
1 – 1/5 not equal to 1/10
If A = 15,
1/6 – 1/10 = 1/15
So, A = 15

Question 38

Three pipes A,B and C can fill a tank from empty to fill in 30 min, 20 mins and 10 min 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 solution R in the liquid in the tank after 3 minutes?

A	1/11
B	5/11
C	6/11
D	8/11

Question 38 Explanation:

Part of tank filled in 3 minutes
= 3 * [(1/30)+(1/20)+(1/10)]
= 11/20
Part of tank filled by C in 3 minutes
= 3/10
Ratio = 3/10 : 11/20
= 6: 11

Question 39

Two taps can fill a cistern in 30 and 40 minutes respectively. If both the taps are opened simultaneously then the approximate time taken to fill the cistern is

A	17 minutes
B	12 minutes
C	19 minutes
D	21 minutes

Question 39 Explanation:

Let the time taken to fill the cistern be x minutes
1/x = 1/30 = 1/40 = 7/120
X= 120/7 = 17. 14 minutes

Question 40

A pipe P can fill a tank in 16 mins and the other pipe Q can empty the whole tank in 32 mins. If both P and Q are opened simultaneously, then the time taken to fill the tank is

A	16 mins
B	32 mins
C	48 mins
D	40 mins

Question 40 Explanation:

Let the time taken to fill the tank be x minutes
1/x = 1/P – 1/Q
= 1/16 – 1/32
= 1/32
X= 32 mins

Question 41

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

A	8 hrs
B	6 hrs
C	2 hrs
D	1 hrs

Question 41 Explanation:

1/A + 1/B – ¼
B= A+6
We can check the options to find the answer
If A=8,
1/8 + 1/1 4 not equal to ¼
If A = 6,
1/6 + 1/12 = ¼
So, A = 6

Question 42

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?

A	3.5
B	2
C	3
D	2.5

Question 42 Explanation:

Part of tank filled in 1 hour when all the pipes are open
= (1/A) + (1/B) + (1/C)
=(1/5) + (1/10) + (1/30)
= 1/3
The tank will be filled in 3 hours

Question 43

A Pump can fill a tank with water in 2 hours because of a leak, it took 7/3 hours to fill the tank. The leak can drain out the tank in

A	8 hrs
B	14 hrs
C	7 hrs
D	13/3

Question 43 Explanation:

Let the leak take x hours to drain out the tank
½ - 1/x = 3/7
1/x = ½ - 3/7 = 1/14
X= 14

Question 44

A water tank is two- fifth full. Pipe A can fill the tank in 10 mins and pipe B can empty it in 6 mins. If both the pipes are open, how long will it take to empty or fill the tank completely?

A	6mins to fill
B	9 mins to fill
C	6 mins to empty
D	9 mins to empty

Question 44 Explanation:

Part of tank filled by A in 1minute = 1/10
Part of tank emptied by B in 1 minute = 1/6
The rate at which pipe B empties is higher than the rate at which the pipe A fills the tank
Part of tank emptied in 1minute when A and B are opened = 1/6 – 1/10
= 1/ 15
Time taken to empty 2/5th of the tank
= 2/5 / 1/15
= 6 minutes

Question 45

A tank can be filled by a tap in 20 mins and by another tap in 60 mins. Both the taps are kept open for 10 mins and then the first tap is shut off. After this, the tank will be completely filled in?

A	10 mins
B	15 mins
C	12 mins
D	20 mins

Question 45 Explanation:

Part of tank filled by both the taps in 1 minute = (1/20) + (1/60)
= 1/15
Part of tank filled by both the taps in 10 minutes = 2/3
The remaining 1/3 of the tank is filled by the second tap alone.
Time taken to fill 1/3 of the tank = (1/3) /(1/60) = 20 minutes

Question 46

12 Buckets of water fill a tank when the capacity of each bucket is 13.5 liters. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 liters?

A	8
B	15
C	16
D	18

Question 46 Explanation:

Capacity of the tank = (12*13.5) liters = 162 litres
Number of 9 liters buckets needed = (162/9) = 18

Question 47

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, the time that the leak will take to empty it, is

A	60 hrs
B	80 hrs
C	70 hrs
D	90 hrs

Question 47 Explanation:

Part of the cistern emptied by the leak in 1 hour = (1/9 - 1/10) = 1/90
The leak will empty the cistern in 90 hrs

Question 48

To fill a cistern, pipes A,B and C take 20 minutes, 15 minutes and 12 minutes respectively. The time taken by the three pipes together to fill the cistern is

A	5mins
B	12 mins
C	10 mins
D	15(2/3) mins

Question 48 Explanation:

Part of tank filled by A,B and C in 1 minute
= 1/20 + 1/15 + 1/12
= 1/5
The cistern will be filled in 5 mins

Question 49

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?

A	7mins 45 sec
B	8 mins 5 sec
C	7 mins 15 sec
D	8 mins 15 sec

Question 49 Explanation:

Part of the bucket filled by A and B in 1 minute
= (1/A) + (1/B)
= 3/20
Part of the bucket filled by A and B in 3 minutes = 9/20
The remaining 11/20 of the bucket is filled by B alone Time taken = (11/20) / (1/15)
= 33/4 minutes
= 8 mins 15 seconds

Question 50

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 the tank will be filled?

A	7 hrs
B	7hrs 30 mins
C	8 hrs
D	8 hrs 30 mins

Question 50 Explanation:

Part of tank filled in 1 hour = (1/10) + (1/12) + (1/20)
= 2/15
The tank will be filled in 15/2 hrs
= 7 hrs 30 minutes

Question 51

Two taps A and B can fill a tank in 10 hours and 15 hours respectively. If both the taps are opened together, the tank will be full in

A	5 hrs
B	12.5 hrs
C	6 hrs
D	7.5 hrs

Question 51 Explanation:

Part of tank filled by A and B in 1 hour = (1/10) + (1/15)
= 1/6
The tank will be filled in 6 hours

Question 52

A tap can fill a cistern in 2 hours and another tap can empty the cistern in 3 hours. How long will it take to fill the cistern if both the taps are opened?

A	5 hrs
B	7 hrs
C	6 hrs
D	8 hrs

Question 52 Explanation:

Part of the cistern filled by the first tap in 1 hour = ½
Part of the cistern filled by the second tap in 1 hour = 1/3
Part of the cistern filled in 1 hour when both the taps are opened = (1/2) – (1/3)
= 1/6
The cistern will be filled in 6 hours

Question 53

A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. 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 the waste pipe take to empty the full cistern?

A	8 minutes
B	12 minutes
C	10 minutes
D	16 minutes

Question 53 Explanation:

Part of tank emptied by the waste pipe in 1 minute = (1/12) + (1/15) – (1/20)
= 1/10
The waste pipe takes 10 minutes to empty the cistern

Question 54

An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 minutes to fill the tank. The leak can drain out all the water of the tank in

A	10 hrs 30 mins
B	21 hours
C	12 hours
D	24 hours

Question 54 Explanation:

3hrs 30 minutes
= 3.5 hours
= 7/2 hours
Work done by the leak in 1 hour
= (1/3) – (2/7)
= 1/21
The leak will empty the tank in 21 hours

Question 55

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 hrs
B	20 hrs
C	35 hrs
D	cannot be determined

Question 55 Explanation:

1/A + 1/B + 1/C= 1/5
Let the time taken by A to fill the tank be X hours
B is twice as fast as A
Time taken by B = x/2 minutes
C is twice as fast as B
Time taken by C = x/4 minutes
1/x + 2/x + 4/x = 1/5
X= 35

Question 56

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

A	10 mins 20sec
B	11mins 45 sec
C	12mins 30
D	15 mins

Question 56 Explanation:

B is used for x minutes. A and B are used together for the next x minutes
Part of tank filled by B in x minutes = x/40
Part of tank filled by A and B in 1 minute = 1/60 + 1/40
= 1/24
Part of tank filled by A and B in x minutes= x/24
x/40 + x/24 = 1
8x = 120
X = 15
The total time taken is 2x = 30 minutes

Question 57

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 mins
B	20 mins
C	27.5 mins
D	30 mins

Question 57 Explanation:

Let the time taken to fill the tanker be 2x minutes
Part of tank filled by B in x minutes = x/40
Part of tank filled by A and B in x minutes = x/40 + x/60
x/40 + x/40 +x/60 =1
x= 15
2x = 30

Question 58

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hour, 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

Question 58 Explanation:

Part of the tank filled by A, B and C in 2 hours = 2/6 = 1/3
The remaining 2/3 of the tank is filled by A and B in 7 hours
Part of tank filled by A and B in 1 hour = (2/3) / 7 = 2/21
1/C = 1/6 – 2/21
= 3/42
= 1/14
C alone can fill the tank in 14 hours

Question 59

A pipe can fill a tank in 6 hours. After three fourth the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?

A	4hrs 30 mins
B	5hrs
C	5 hrs 15 mins
D	5 hrs 30 mins

Question 59 Explanation:

Part of tank filled by 3 pipes in 1 hour = 3/6 = ½
1/4th of the tank is filled by 3 pipes in ½ hours
Time taken by the pipe to fill ¾ of the tank = 6*3/4 = 9/2
Total time taken = ½ + 9/2 = 5 hours

Question 60

If two pipes C and D can together fill a tank in 36 minutes and pipe C alone takes 1 hour to fill the tank, find the time taken by pipe D alone to fill the tank?

A	72 mins
B	80 mins
C	100 mins
D	90 mins

Question 60 Explanation:

Answer: Option D
1/D = 1/36 – 1/60 = 1/90
D alone takes 90 minutes to fill the tank

Question 61

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours. C is closed A and B can fill the remaining pair in 7 hours. The number of hours taken by C alone to fill the tank is?

A	15
B	12
C	14
D	41

Question 61 Explanation:

Part filled in 2 hours = 2/6 = 1/3
Remaining part = 1-1/3 = 2/3
(A+B)’s 1 hour work = 2/21
C’s 1 hour work = [(A+B+C)’s 1 hour work – (A+B)’s1 hour work]
= (1/6 – 2/21) = 1/14
C alone can fill the tank in 14 hours

Question 62

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

Question 62 Explanation:

Work done by the waste pipe in 1 minute = 1/15 – (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 3 gallons
Volume of whole = 3 * 40 = 120 gallons

Question 63

Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 3 minutes A is turned off. After how much more time will the cistern be filled?

A	3 ¼ min
B	5 ¼ min
C	8 ¼ min
D	9 ¼ min

Question 63 Explanation:

3/12 +(3+X)/15 =1
X= 8 ¼

Question 64

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 per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?

A	5260 liters
B	5760 liters
C	5846 liters
D	6970 liters

Question 64 Explanation:

1/x – 1/6 = -1/8
X= 24 hrs
24 * 60 * 4 =5760

Question 65

A cistern has three pipes A,B and C. The pipes And B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipe are opened in order at 1,2 and 3 A.M. When will the cistern be empty?

A	4PM
B	5.30 PM
C	6PM
D	5 PM

Question 65 Explanation:

1 to 2 = ¼
2 to 3 = ¼ + 1/5 = 9/20
After 3AM = ¼ + 1/5 – ½ = - 1/20
¼ + 9/20 = 14/20
1 hr -----1/20
? --------14/20
14 hours  5 PM

Question 66

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?

A	5/11
B	6/11
C	7/11
D	8/11

Question 66 Explanation:

Question 67

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:

A	1 13/17 hours
B	2 8/11
C	3 9/17
D	4 1/2 1

Question 67 Explanation:

Net part filled in 1 hour 1 + 1 - 1 = 17 . 5 6 12 60 The tank will be full in 60 hours i.e., 3 9 hours. 17 17

Question 68

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

A	4 1/3 Hours
B	7 hours
C	8 hours
D	14 hours

Question 68 Explanation:

Work done by the leak in 1 hour = 1 - 3 = 1 . 2 7 14 Leak will empty the tank in 14 hrs.

Question 69

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.

Question 69 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. x 2 + 1 + (30 - x). 2 = 1 75 45 75 11x + (60 -2x) = 1 225 75 11x + 180 - 6x = 225. x = 9.

Question 70

A	6 hours
B	10 hours
C	15 hours
D	30 hours

Question 70 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 = 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]

Question 71

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.

Question 71 Explanation:

Let the slower pipe alone fill the tank in x minutes. Then, faster pipe will fill it in x minutes. 3 1 + 3 = 1 x x 36 4 = 1 x 36 x = 144 min.

Question 72

A	15 min
B	20 min
C	27.5 min
D	30 min

Question 72 Explanation:

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 = 1 2 24 40 x x 1 = 1 2 15 x = 30 min.

Question 73

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

Question 73 Explanation:

Time taken by one tap to fill half of the tank = 3 hrs. Part filled by the four taps in 1 hour = 4 x 1 = 2 . 6 3 Remaining part = 1 - 1 = 1 . 2 2 2 : 1 :: 1 : x 3 2 x = 1 x 1 x 3 = 3 hours i.e., 45 mins. 2 2 4 So, total time taken = 3 hrs. 45 mins.

Question 74

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:

A	6 hours
B	6 2/3 hours
C	7 hours
D	7 1/2 houurs

Question 74 Explanation:

c) 7 hours d) 7 1 hours 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 x 17 = 17 . 60 20 Remaining part = 1 - 17 = 3 . 20 20 Now, it is the turn of A and B and 3 part is filled by A and B in 1 hour. 20 Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.

Question 75

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

Question 75 Explanation:

Part filled in 2 hours = 2 = 1 6 3 Remaining part = 1 - 1 = 2 . 3 3 (A + B)'s 7 hour's work = 2 3 (A + B)'s 1 hour's work = 2 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 C alone can fill the tank in 14 hours.

Question 76

A	60 gallons
B	100 gallons
C	120 gallons
D	180 gallons

Question 76 Explanation:

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 of 1 part = 3 gallons. 40 Volume of whole = (3 x 40) gallons = 120 gallons.

Question 77

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

Question 77 Explanation:

Suppose pipe A alone takes x hours to fill the tank. Then, pipes B and C will take x and x hours respectively to fill the tank. 2 4 1 + 2 + 4 = 1 x x x 5 7 = 1 x 5 x = 35 hrs.

Question 78

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

Question 78 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 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]

Question 79

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	15 min
D	50 min

Question 79 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.

Question 80

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.

Question 80 Explanation:

Part filled in 4 minutes = 4 1 + 1 = 7 . 15 20 15 Remaining part = 1 - 7 = 8 . 15 15 Part filled by B in 1 minute = 1 20 1 : 8 :: 1 : x 20 15 x = 8 x 1 x 20 = 10 2 min = 10 min. 40 sec. 15 3 The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.

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Pipes and Cisterns

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