Pipe and Cistern

29 April 2020


Pipes and Cisterns form an important part of the quantitative aptitude section. Pipes and cisterns problems are almost the same as those of Time and work problems. Here we have provided variety of fully solved questions of Pipes and cistern.


Practice Questions For Pipe and Cistern

Q1)  A pump can fill a tank with water in 2 hours. Because of a leak, it took 8/3 hours to fill the tank. The leak can drain all the water of the tank in

A) 9 hours

B) 8 hours

C) 10 hours

D) 6 hours

Solution :


Q2) 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) 7/11

C) 6/11

D) 8/11

Solution :


Q3) 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. Time required by the first pipe to fill the tank is

A) 6 hours

B) 15 hours

C) 10 hours

D) 30 hours

Solution :


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Q4) 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) 4 hours

B) 2 hours

C) 6 hours

D) 3 hours

Solution :


Q5) Two outlet pipes A and B are connected to a full tank. Pipe A alone can empty the tank in 10 minutes and pipe B alone can empty the tank in 30 minutes. If both are opened together, how much time will it take to empty the tank completely?

A) 7 minutes

B) 7 minutes 30 seconds

C) 6 minutes

D) 6 minutes 3 seconds

Solution:

Let the capacity of the tank be LCM(10, 30) = 30 units
=> Efficiency of pipe A = 30 / 10 = 3 units / minute
=> Efficiency of pipe A = 30 / 30 = 1 units / minute
=> Combined efficiency of pipe A and pipe B = 4 units / minute  
Therefore, time required to empty the tank if both pipes work = 30 / 4 = 7 minutes 30 seconds

Q6) Two pipes A and B attached to a swimming pool can fill the pool in 20 minutes and 30 minutes respectively working alone. Both were opened together but due to malfunctioning of motor of pipe A, it had to be shut down after two minutes but B continued to work till the swimming pool was filled completely. Find the total time taken to fill the pool.

A) 20

B) 22

C) 25

D) 27

Solution :

Let the capacity of the pool be LCM(20, 30) = 60 units.
=> Efficiency of pipe A = 60 / 20 = 3 units / minute
=> Efficiency of pipe B = 60 / 30 = 2 units / minute
=> Combined efficiency of pipe A and pipe B = 5 units / minute Now, the pool is filled with the efficiency of 5 units / minute for two minutes.
=> Pool filled in two minutes = 10 units
=> Pool still empty = 60 - 10 = 50 units This 50 units is filled by B alone.
=> Time required to fill these 50 units = 50 / 2 = 25 minutes  
Therefore, total time required to fill the pool = 2 + 25 = 27 minutes

Q7) Three pipes A, B and C were opened to fill a cistern. Working alone, A, B and C require 12, 15 and 20 minutes respectively.After 4 minutes of working together, A got blocked and after another 1 minute, B also got blocked. C continued to work till the end and the cistern got completely filled. What is the total time taken to fill the cistern ?

A) 6 minutes

B) 6 minutes 15 seconds

C) 6 minutes 40 seconds

D) 6 minutes 50 seconds

Solution : 

Let the capacity of the cistern be LCM(12, 15, 20) = 60 units.
=> Efficiency of pipe A = 60 / 12 = 5 units / minute
=> Efficiency of pipe B = 60 / 15 = 4 units / minute
=> Efficiency of pipe C = 60 / 20 = 3 units / minute
=> Combined efficiency of pipe A, pipe B and pipe C = 12 units / minute
Now, the cistern is filled with the efficiency of 12 units / minute for 4 minutes.
=> Pool filled in 4 minutes = 48 units => Pool still empty = 60 – 48 = 12 units Now, A stops working.
=> Combined efficiency of pipe B and pipe C = 7 units / minute
ow, the cistern is filled with the efficiency of 7 units / minute for 1 minute.
=> Pool filled in 1 minute = 7 units => Pool still empty = 12 – 7 = 5 units
Now, B also stops working. These remaining 5 units are filled by C alone.
=> Time required to fill these 5 units = 5 / 3 = 1 minute 40 seconds  
Therefore, total time required to fill the pool = 4 minutes + 1 minutes + 1 minute 40 seconds = 6 minutes 40 seconds

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Q8) Three pipes A, B and C are connected to a tank. Working alone, they require 10 hours, 20 hours and 30 hours respectively. After some time, A is closed and after another 2 hours, B is also closed. C works for another 14 hours so that the tank gets filled completely. Find the time (in hours) after which pipe A was closed.

A) 1

B) 1.5

C) 2

D) 3

Solution :

Let the capacity of the tank be LCM (10, 20, 30) = 60
=> Efficiency of pipe A = 60 / 10 = 6 units / hour
=> Efficiency of pipe B = 60 / 20 = 3 units / hour
=> Efficiency of pipe C = 60 / 30 = 2 units / hour
Now, all three work for some time, say 't' hours.
So, B and C work for 2 more hours after 't' hours and then, C works for another 14 hours.
=> Combined efficiency of pipe A, pipe B and pipe C = 11 units / hour
=> Combined efficiency of pipe B and pipe C = 5 units / hour
 So, we have 11 x t + 5 x 2 + 14 x 2 = 60 => 11 t + 10 + 28 = 60
=> 11 t = 60 - 38 => 11 t = 22 => t = 2   Therefore, A was closed after 2 hours.

Q9)Working alone, two pipes A and B require 9 hours and 6.25 hours more respectively to fill a pool than if they were working together. Find the total time taken to fill the pool if both were working together.

A) 6

B) 6.5

C) 7

D) 7.5

Solution : 

Let the time taken if both were working together be 'n' hours.
=> Time taken by A = n + 9
=> Time taken by B = n + 6.25  
In such kind of problems, we apply the formula : n2 = a x b, where 'a' and 'b' are the extra time taken if both work individually than if both work together.
Therefore, n2 = 9 x 6.25 => n = 3 x 2.5 = 7.5   Thus, working together, pipes A and B require 7.5 hours.

Q10) Three pipes A, B and C were opened to fill a cistern. Working alone, A, B and C require 12, 15 and 20 minutes respectively. Another pipe D, which is a waste pipe, can empty the filled tank in 30 minutes working alone. What is the total time (in minutes) taken to fill the cistern if all the pipes are simultaneously opened ?

A) 5

B) 6

C) 7

D) 8

Solution :

Let the capacity of the cistern be LCM(12, 15, 20, 30) = 60 units.
=> Efficiency of pipe A = 60 / 12 = 5 units / minute
=> Efficiency of pipe B = 60 / 15 = 4 units / minute
=> Efficiency of pipe C = 60 / 20 = 3 units / minute
=> Efficiency of pipe D = 60 / 30 = 2 units / minute
> Combined efficiency of pipe A, pipe B, pipe C and pipe D = 10 units / minute  
Therefore, time required to fill the cistern if all the pipes are opened simultaneously = 60 / 10 = 6 minutes
 

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