Pipes and Cisterns Questions for CAT

Pipes and Cisterns Questions for CAT:

Pipes and cisterns is one of the topics that can be asked from the Time, work, speed and distance. These questions are from CAT previous papers, so these questions are important for CAT aspirants.

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Question 1: A hole can empty a full tank in 60 minutes. To maintain the level of water in the tank, 3 filling pipes of equal efficiency are required. How many more such filling pipes will be required so that an empty tank gets filled in 180 minutes?

a) 0
b) 1
c) 2
d) 3

Question 2: A fill pipe can fill the tank in 15 minutes and a drain pipe can drain the tank in 30 minutes. If a system of ‘x’ pipes (includes both fill and drain pipes) fills the tank in 3 minutes. Find the possible value of ‘x’.

a) 10
b) 16
c) 12
d) 14

Question 3: Five pipes A, B, C, D, and E can fill a tank in 60 minutes, 20 minutes, 30 minutes, 8 minutes, 32 minutes respectively. Out of these five pipes, two have now been converted into emptying pipes such that there efficiency remains the same. When only one of filling pipes and one of the emptying pipes operate, the tank can be filled in 60 minutes while another combination of emptying and filling pipe empties it in $\frac{8}{45}^{th}$ of the time taken by the previous combination to fill the tank. Which pipes are converted into emptying pipes?

a) A and D
b) C and D
c) B and D
d) Cannot be determined

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Question 4: An empty tank can be filled in 70 minutes by water flowing from a pipe of square cross section of side 3 cm at the rate of 4 cm/sec. Now another pipe of a circular cross section is added at the bottom of the tank which empties the tank at the rate of 7 cm/sec. When both the pipes are present the tank when empty gets filled completely in 180 minutes. What is the radius of the circular pipe at the bottom of the tank (in cm)?

a) 1
b) 2
c) 3
d) None of these

Question 5: Three pipes A, B and C can fill an empty tank in 4 hours, 5 hours and 6 hours respectively. There is a hole in the tank, which can empty a full tank in 8 hours. Initially, the tank is empty. A and B are opened. They are closed after half an hour. C is now opened and allowed to run for the next 1 hour. Find the total time required to fill the tank if all three taps are opened simultaneously after the first one and a half hours.

a) 4.11 hours
b) 3.6 hours
c) 3.11 hours
d) 4.6 hours

Answers and Solutions for Pipes and Cisterns Questions for CAT:

Solutions:

1) Answer (B)

Assume the work to be done is 180 units. So the efficiency of the hole is -180/60= -3 units/ min. Now, to maintain the level, 3 filling pipes are required. This means that these 3 filling pipes offset the negative work done by the hole. Thus, efficiency of each filling pipe is +1 unit/min. Now we want an empty tank to be filled in 180 minutes. This means that the efficiency of the whole system should be 180/180= 1 unit/min. With 3 pipes, we already offset the negative work done by the hole. To make the efficiency 1 unit/min, we would need 1 more filling pipe. Thus, the answer is 1.

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2) Answer (D)

In a given time, one fill pipe cancels out two drain pipes, and we require 5 more fill pipes to fill the tank in 3 minutes. So the number of pipes would be in the form of 3x+5.
Among the given options only ‘14’ is in the form of 3x+5.
So the correct option to choose is D.

3) Answer (D)

Let the total work to be done be 480 units (LCM of 60,20,30,8,32)
So the respective efficiencies of different pipes are-
A- 8 units/min (480/60)
B- 24 units/min
C- 16 units/min
D- 60 units/min
E- 15 units/min
Now, one combination of emptying and filling pipe can fill the tank in 60 minutes, i.e. together they can do 480/60=8 units of work per minute.
Out of the combinations possible, only A-C and B-C have a difference of 8 units/min.
So, if A is an emptying the tank and C is a filling it, they will do together 8 units of work per min. When C is an emptying the tank and B is filling it, the work done per minute will be the same 8 units/min.
According to the question, the second combination takes 8/45th of time of first one, i.e 32/3 minutes. Only combination that can do so is when D is the emptying pipe and E is the filling pipe. So among A, B, and C, we cannot know for sure which pipe is the filling one and which one is the emptying one.
Thus, we can’t determine which pipes have been converted to emptying pipes.

4) Answer (A)

Volume of flow of water into the tank per second = Rate of flow * Area of cross section of pipe
In first case with only one pipe, Volume flow per sec = $3^2 \times 4$ = 36 units
In second case, Volume flow per sec = 36 – $ \pi r^2\times7$ = 36- $ 7\pi r^2$ units
Ratio of times taken is the inverse ratio of volumes flow per sec
=> $\frac{70}{180}=\frac{36-7\pi r^2}{36}$
Solving, we get r = 1 cm.

5) Answer (C)

Let the amount of work to be done to either fill an empty tank or empty a full tank be LCM(4,5,6,8) = 5*8*3 = 120 units
Work done by pipe A in one hour = 120/4 = 30 units
Work done by pipe B in one hour = 120/5 = 24 units
Work done by pipe C in one hour = 120/6 = 20 units
Work done by the hole in one hour = 120/8 = 15 units
Work done in the first one and a half hours = 15 + 12 + 20 – (3/2)*15 = 47 – 22.5 = 24.5 units
Work remaining = 120 – 24.5 = 95.5 units
Work done by all the taps together in 1 hour when they are opened simultaneously = 30 + 24 + 20 – 15 = 59 units
So, time required to fill the remaining tank = 95.5/59 hours = 1.61 hours
So, total time required to fill the empty tank = 1.5 + 1.61 = 3.11 hours

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