Pipes and Cisterns: Basic Concepts, Formulas

Note- Problems on Pipes and Cisterns are same as that of Time and Work.

Important Concepts

If a pipe fills a tank in x hours, then the part filled in 1 hour = $\frac { 1 }{ x }$

If a pipe empty a tank in x hours, then the part of tank emptied in 1 hour = $\frac { 1 }{ x }$ hours

If a Pipe A alone fills a tank in x hours and another Pipe B alone fills in y hours.

Then the time taken to fill the tank when both pipes are open = $\frac { xy }{ x+y }$ hours.

If two pipes A and B together fills a tank in x hours and A alone fills in y hours

Then the time is taken by B to fill the tank = $\frac { xy }{ y-x }$ hours

If a Pipe A alone empties a tank in x hours and another Pipe B alone empty it in y hours.

Then the time taken to empty the tank when both pipes are open = $\frac { xy }{ x+y }$  hours

If A, B, and C alone fills a tank in x, y, and z hours, then the time is taken to fill the tank when all are open= $\frac { xyz }{ (xy+yz+zx) }$ hours

If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (x>y), then the net part emptied in 1 hour will be= $\frac { 1 }{ y } -\frac { 1 }{ x }$

Example-

Two pipes can fill a tank in 24 hours and 36 hours respectively. If both the pipes are opened at the same time, then how much time will be taken to fill the tank?

Solution-

Pipe A in 1 hour = 1/24

Pipe B in 1 hour = 1/36

Pipe A and B together in 1 hour = (1/24) + (1/ 36) = 1/9

So, Both Pipes will take 9 hours to fill the tank. (Reason- Check Statement 1)