Pipes and Cistern

Pipes and cisterns are important quantitative aptitude topics similar to time and work concepts. The formula for pipes and cisterns is also related to Time and work. It is common in various competitive exams, including SSC, RRB, banking, and management exams. Common exam questions are several problems, such as how long it takes to fill an empty tank, what happens if one pipe is closed, and how long it will take for another pipe to fill the tank. As a result, understanding every concept of pipes and cisterns becomes critical so that you can easily solve the related questions.

Pipes and cistern 

Pipes and cistern is a quantitative aptitude concept similar to Time and work.

The pipe is linked to a cistern or tank, and the water is filled. There are two kinds of pipes discussed: inlet pipe and outlet pipe. 

Inlet pipe: An inlet is a pipe that links to a tank to fill it. 

Outlet pipe: An outlet is a pipe attached to an empty tank. 

Like the work and time concept, the work here represents the portion of the cistern to be filled or empty, and the time is to complete these tasks. So, the pipes and cisterns formula is the flow rate multiplied with Time to give the capacity to fill the tank. 

Some of the points to remember in the concept are discussed below. 

• Consider a tank having an inlet linked to it and try to fill it in x hours; the fraction of the large tank in 60 minutes is equal to 1/x.
• Consider a tank having an outlet linked to it and try to fill it in; part of the tank emptied in 60 minutes is = 1/b.

• A tank can be filled in x hours by an inlet and emptied in y hours by an outlet. If we open both pipes simultaneously and y > x, the total amount of large tank in one 60 minutes is given by; (1/x-1/y). As a result, when we open both pipes, the time required to fill up the entire tank is given. (xy/y-x) 

• If X is larger than Y, more water goes out of the chamber than into it. Furthermore, the net portion of the water reservoir emptied in 60 minutes is given by;

            (1/Y-1/X) .As a result, when both      pipes are open, the Time required to unload the full tank is provided by 

(YX/X-Y) 

• In A tank, there are two inlets, and one inlet fills the tank in x hours, whereas another inlet fills the same cistern in y hours. However,  If both inlets are opened simultaneously, the net portion of a tank filled in one 60 minutes is (1/x+1/y), the Time taken to fill the complete tank by both inlets is (xy/y+x) 

• Three inlets, A, B, and C, can fill the tank in x, y, and z hours, respectively. If all three of the inlets are started opening at the same time, the time required to fill up the tank is (x+y+z/xy+yz+zx) 
• Two inlet pipes are present that can fill the cistern in x and y hours, respectively, and an outlet tank is also present, which can efficiently empty the tank in z hours. However, If we open all three pipes together, the portion of a tank filled in 60 minutes is (1/x+1/y-1/z). Also, the Time taken to fill the tank when all the pipes are working is given by; (xyz/yz+xz+xy) 

• A pipe fills a tank in x hours, but it can only fill it in y hours due to leaks in the bottom. The amount of time required for the leak to the vacant tank is provided by; (xyz/yz+zx-XY) 

• An inlet A is x times better than an inlet B and takes y mins less to fill a tank when we open both the pipes simultaneously.; XY/(x-1) ^2

Let’s discuss some of the pipes and cisterns questions.

Pipes P and Q can fill the cistern in 37.5 and 45 minutes, respectively. If both pipes are started opening, the cistern would be filled in less than half an hour if pipe Q is turned off afterwards.

We will first take the LCM of times taken by pipes to fill the cistern in this problem. As the lcm of both is 225, it is the cistern’s capacity. 

Now we need to calculate the efficiency of both the pipes as efficiency is divided by Time. 

Pipe P capacity= 225/37.5= 6

Pipe Q Capacity= 225/45= 5

           Pipe A runs for 30 minutes.

           6× 30 = 180 units

This means that  pipe P filled 180 units of the tank in 30 minutes

The remaining cistern is filled by Q,

Remaining quantity left to fill = 225 – 180

That is 45 units. 

Now, to fill the remaining tank, 

Remaining quantity to fill/ efficiency of PipeQ 

total Time is taken by PipeQ = 45/5

that is 9 minutes

Conclusion

One of the key concepts in quantitative aptitude is pipes and cisterns. The concepts and the formula for pipes and cisterns are similar to work and Time. A problem that arises from this chapter is that two pipes can fill a cistern in a certain amount of time, and if one of them is closed, how long will the other one take to fill the tank. And if you are preparing for competitive exams such as banking, SSC, RRB, and management exams, you should study the chapter thoroughly because many questions are asked each year.