Aptitude Pipes And Cistern Tutorials & Tricks

Pipes And Cistern Tutorials & Tricks

Formula for finding out Pipes and Cisterns

1. Inlet: A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet. Outlet: A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.

2. If a pipe can fill a tank in x hours, then: part filled in 1 hour = 1/x

3.If a pipe can empty a tank in y hours, then: part emptied in 1 hour = 1/y

4. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then the net part filled in 1 hour = (1/x)-(1/y)

5.If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes, then the net part emptied in 1 hour = (1/y)-(1/x)

6. Rule 1:a pipe can fill a tank in x hours, then the part filled in 1 hour = 1 / x

Rule 2:If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours, then the net part filled in 1 hour, when both the pipes are opened : ((1/x)-(1/y)) Time taken to fill the tank, when both the pipes are opened : (xy/(y-x))

Rule 3:: If a pipe can fill a tank in x hours and another fill the same tank in y hours, then the net part filled in 1 hr, when both pipes are opened: ((1/x)+(1/y)) So time to fill the tank will be : (xy/(y-x))

Rule 4:If a pipe fills a tank in x hrs and another fills the same tank in y hrs, but a third empties the full tank in z hrs and all of them are opened together, the net part filled in 1 hr : ((1/x)+(1/y)-(1/z)) So time taken to fill the tank : (xyz/(yz+xz-y))

Sample Example

Ex

A cistern is normally filled in 8 hrs, but it takes four hrs longer to fill beacuse of a leak in the bottom. If the cistern is full , how much time the leak will empty it ?

A

 : Let the leak will empty the tank in x hrs. Then part of cistern filled in 1 hr = ( 1 / 8 ) - ( 1 / x ) = x - 8 / 8x So cistern will completly filled in 8x / x - 8 8x/(x-8) = 8+4 =12, x=24 hrs

Ex

Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, Pipe A is turned off. What is the total time required to fill the tank ?

A

 Part of tank filled by A + B in 1 minute = ( 1 / 15 + 1 / 20 ) So tank filled by A + B in 4 minute = 4 ( 1 / 15 + 1 / 20 ) = 7 / 15 Part remaning = 1 - ( 7 / 15 ) = 8 / 15 1 / 20 part is filled by B in 1 minute So, 8 / 15 part will be filled in = ( 20 / 1 )* ( 8 / 15 ) = 32 / 3 = 10 minutes 40 sec. 

Ex

Three pipes A, B and C can fill a tank in 6 hours. After working together for 2 hours, C is closed and A and B can fill the remaning part in 7 hours. Find the number of hours taken by C alone to fill the tank ?

A

 Work done by A+B+C in 2 hours = 2 /6 = 1 / 3 So, work remaning = 1- ( 1/ 3 ) = 2 / 3 Now (A + B)'s 7 hour work = 2 / 3 ( A + B )'s 1 hour work will be = 2 / 21 So C's 1 hour work will be = 1 hour work of (A+B+C) - 1 hour work of (A+B) = ( 1/ 6) - ( 2/ 21) = 1 / 14 So C alone can fill the tank in 14 hours