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Wednesday, July 15, 2015

Simple and Shortcut Trick & Concept to Solve Pipes and Cistern

                                           Pipes & Cistern

This topic is very important to major competitive exams. You will usually have a problems where they give two or more pipes that Simultaneously fill and empty the tanks.  This thing is impossible to solve but the few basics we will be able to solve this like a breeze.

This is known as a Cistern  or a Tank, its also called a Vessel  in some problems.

You have an two type of pipes 1) Inlet Pipes & 2) outlet Pipes.
(1)  Inlet Pipes : Fills the tank
(2)  Outlet Pipes : Empty the tanks.

Very important point to note that Inlet pipes work +ve Work and and Outlet pipes does – ve work.

So Lets solve some simple problem.
Problem 1: A pipe ‘A’ fill a tank in 36 hrs and pipe ‘B’ fills the same in 45 hrs. How much time will the two pipes to fill the tank if both pipes  operate simultaneously?
Solution :
A very important rule in pipes and cisterns “ If a pipe fill a tank in ‘X’ hours, then every hour 1/X th part of the tank is filled ! “
                     A’s Fills a tank in 36 hrs, so every 1/36 hour  
                     B’s Fills a tank in 45 hrs, so every 1/45 hour  

So the  Combine work will be = 1/36 + 1/45 , Both pipes are inlet pipes so they will do the +ve works.
                Take LCM first = (5+4)/180 = 9/180 = 1/20 th tanks filled every hour

Hence the tank will fill in 20 hours.
If there is simple modification, suppose B as a outlet Pipes.

So for calculations of outlet pipes  1/36 - 1/45 = (5-4)/180 = 1/180.
So the answer will be 18 hrs.

Problem 2: Two pipes can fill the tank in 10hours and 12 hours respectively while a third pipes empty the tank in 20 hours. If all the three pipes operate simultaneously, in how time will the tank to filled?
Solutions : 
1’st Fills a tank in 10 hrs, so every hour 1/10.  
2’nd Fills a tank in 12 hrs, so every hour 1/12.  
3’rd empty a tank in 20 hrs, so every hour -1/20.

So all simultaneously = 1/10 + 1/12 - 1/20

if you take LCM will be (6+5-3)/60 = 8/60 = 2/15   filled by every hr.

then to fill the tank total time will taken is 15/2  just inverse. Or  7 *1/2hrs. Or  7 hrs .30 min