Pipes And Cisterns in Mathematics

 Pipes & Cisterns  in Mathematics 

This article will introduce you to the idea of pipes and cisterns as they are presented in competitive exams, as well as the kind of questions that may be given, some key formulas for answering them, and a few practise problems to help you grasp the subject better.
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✅ Basic:- Problems on Pipes and Cisterns are based on the basic concept of time and work. Pipes are connected to a tank or cistern and are used to fill or empty the tank or cistern. In pipe and cistern, the work is done in form of filling or emptying a cistern/tank.

👉Types Of Pipes :-

 ☑   Inlet pipe It fills a tank/cistern/reservoir. 

 ☑   Outlet pipe It empties a tank/cistern/reservoir.

✅Note :-  

  

 👉 If a pipe cab fill/empty a tank in 'm' h , then the part of  tank filled /emptied in 1h = 1/m . 

 

 ☑ Example : A pipe can fill/empty '1/m' part of a tank in 1 h, then the volume of tank filled in 1 h = 1/7

 👉 If a pipe can fill /empty '1/m' part of a tank in 7 h then  it can fill/empty the whole tank in 'm' h.

☑ Example : If a pipe can fill 1/5 part of a tank in 1 h then it can fill the whole tank in 5h .

👉Generally , time taken to fill a tank is taken positive (+ve) and time taken to empty a tank is taken negative (-ve). 

👉 If a pipe fills a tank in 'm' 'h' and an another pipe fills in 'n' 'h' . Then , part filled by both pipes in 1 h = 1/m +1/n.

✅Example Of The Math

👉 1. An outlet pipe can empty a cistern in 5h , In what time will the pipe empty 2/5 part of the cistern ?

✔Answer:-  Time taken to empty full cistern = 5h

                     Time taken to empty 2/5 part of the cistern = 2/5 *5 = 2h 

👉 2 If a pipe can fill a tank in 2 h and another pipe can fill the same tank in 6 h, then what part of a tank will be filled by both the pipes in 1 h, if they are opened simultaneously? 

✔Answer:-  In 1h , part filled by 1st pipe = 1/m = 1/2

                    In 1h part filled by 2nd pipe = 1/n = 1/6

                   .'. In 1h , part filled by both the pipes together = (1/m+1/n)

                                                                                                   = (1/2+1/6)

                                                                                                   = (3+1)/6 = 4/6 =2/3 part ✔ 

👉3 When opened separately, the two pipelines P and Q may fill the tank in 20 and 30 hours, respectively. How long would it take to fill the tank if both lines are opened at once?

Answer 

Pipe fills a portion of the tank. P = 1/20 in 1 hour. Pipe Q filled 1/30 of the tank in an hour.

Tank filled in 1 hour by both pipes: 1/20 + 1/30 = 5/60 = 1/12

Both will fill the tank to capacity in 12 hours.

Pipe A can fill a tank in 5 hours, while Pipe B can empty it in 8 hours, respectively. How long will it take the tank to fill halfway?