# Pipes and Cisterns Questions Set 2

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Questions on Pipes and Cisterns with solutions

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## Pipes and Cisterns Questions Set 2

Q.1. Two pipes A,B can fill 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 min?

1. 6 minutes
2. 7 minutes
3. 8 minutes
4. 9 minutes

Let B be closed after x min. then ,

Part filled by (A+B) in x min + part filled by  A in (18-x) min = 1

Therefore x*((1/24)+(1/32))+(18-x)*(1/24) = 1

(7x/96) + ((18-x)/24) = 1.

7x +4*(18-x) = 96

x = 8 minutes

Hence, be must be closed after 8 minutes

Q.2. 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

1. 8 hours
2. 10 hours
3. 12 hours
4. 15 hours

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/x + 1/(x-5) = 1/(x-9)

(2x - 5) (x - 9) = x(x - 5)

x2 - 18x +45 = 0

x = 15

Q.3. 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

1. 100 gallons
2. 120 gallons
3. 140 gallons
4. 160 gallons

Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = -1/40

-ve sign means emptying

Volume of 1/40 part = 3 gallons

Volume of whole = (3*40) gallons = 120 gallons

Q.4.  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?

1. 2 hours
2. 4 hours
3. 6 hours
4. 8 hours

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

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

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

x2 - 2x - 24 = 0

(x -6)(x + 4) = 0

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

Q.5. 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?

1. 14 min 10 sec
2. 14 min 40 sec
3. 12 min 20 sec
4. 15 min 30 sec

Part filled in 4 minutes = 4 (1/15 + 1/20) = 7/15

Remaining part = (1 - 7/15) = 8/15

Part filled by b in 1 minute = 1/20

1/20 : 8/15 = 1 : x

x = 32/3 min = 10 min 40 sec

Tank will be full in (4 min + 10 min + 40 sec) = 14 min 40 sec

Q.6. 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

1. 82 min
2. 104 min
3. 144 min
4. 156 min

Let the slower pipe alone fill the tank in x minutes.

Then faster pipe will fit it in x/3 minutes.

1/x + 3/x = 1/36

4/x = 1/36

x = 144 min

Q.7. 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

1. 12
2. 14
3. 16
4. 18

Part filled in 2 hours = 2/6 = 1/3

Remaining part = 1 - 1/3 = 2/3

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

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

C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work } = 1/6 - 2/21 = 1/14

C alone can fill the tank in 14 hours

Q.8.There is a leak in the bottom of the tank. This leak can empty a full tank in 8 hours. When the tank is full, a tap is opened into the tank which admit 6 liters per hour and the tank is now emptied in 12 hours. What is the capacity of the tank?

1. 8.8 liters
2. 36 liters
3. 144 liters
4. 172 liters

Since the leak can empty the tank in 8 hours,

In one hour, part of the tank emptied by the leak = 1/8

Also, after opening the tap, in one hour, part of the tank emptied = 1/12

Let the tap can fill the tank in x hours. Therefore, In one hour, part of the tank filled by the tap = 1/x

As per question, (1/x) – (1/8) = 1/12

Or x = 24

Since the tap admits 6 liters of water per hour, it will admit (6*24) =144 liters of water in 24 hours, which should be the capacity of the tank.

Q.9. A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?

1. 480 liters
2. 600 liters
3. 720 liters
4. 800 liters

1/x - 1/20 = -1/24

x = 120

120 * 4 = 480

Q.10. 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?

1. 3 hrs 15 min
2. 3 hrs 45 min
3. 4 hrs 45  min
4. 4 hrs 15 min

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

Part filled by the taps in 1 hour = 4 * 1/6 = 2/3

Remaining part = 1 - 1/2 = 1/2

2/3 : 1/2 :: 1 : x

x = 1/2 * 1 * 3/2 = 3/4 hrs. i.e., 45 min

So, total time taken = 3 hrs 45 min.

For any queries or doubts refer to comment section mentioning question number  with doubt