Pipes & Cisterns : - These problems are almost the same as those of Time and work problems. Thus, if a pipe fills a tank in 6 hrs, then the pipe fills 1/6th of the tank in hour.
There is one difference that pipes & cisterns problems is that there are outlets as well as inlets. Thus, there are agents (the outlets) which perform negative work too. The rest of the process is almost similar.
Inlet : A pipe connected with a tank or reservoir for filling is called as inlet
Outlet : A pipe connected with a tank and used for empties it is called outlet.
Concepts and Tricks :
- If a pipe can fill a tank in x hours, then the part filled in 1 hour = 1/x
- 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:
(x×y/y-x)
- 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:
[x×y/(x+y)]
- 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-xy)
Eg. Two pipes A & B can fill a tank in 45 hrs & 36 hrs. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
Solution: Part filled by A alone in 1 hr = 1/45
Part filled by B alone in 1 hr = 1/36
Part filled by (A +B) in 1 hr = (1/45+1/36)= 9/180=1/20
Hence, both the pipes together will fill the tank in 20 hours.
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