**Pipes and cisterns 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 1 hr. the only difference with Pipes and 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**: An inlet pipe is connected with a tank and it fills tank.

**OUTLET:**A outlet pipe is connected with a tank and it empties tank.

### Formulae

**(i)**If a pipe can fill a tank in m hrs, then the part filled in 1 hr =1/m.

**(ii)**If a pipe can empty a tank in n hrs, then the part of the full tank emptied in 1 hr = 1/n .

**(iii)**If a pipe can fill a tank in m hrs and the another pipe can empty the full tank in n hrs, then the net part filled in 1 hr, when both the pipes are opened =[1/m- 1/n]

∴ Time taken to fill the tank, when both the pipes are opened = mn/( n-m)

**(iv)**If a pipe can fill a tank in m hrs and another can fill the same tank in n hrs, then the net part filled in 1 hr, when both the pipes are opened = [1/n- 1/m]

∴ Time taken to fill the tank = mn/(n-m)

**(v)**If a pipe fills a tank in m hrs and another fills the same tank in n hrs, but a third one empties the full tank in p hrs, and all of them are opened together,

the net part filled in 1 hr = [1/m+ 1/n-1/p]

∴ Time taken to fill the tank =mnp/(np+mp-mn) hrs.

**(vi)**A pipe can fill a tank in m hrs. Due to a leak in the bottom it is filled in n hrs. if the tank is full, the time taken by the leak to empty the tank = mn/(n-m) hrs.

But x can’t be –ve, hence the faster pipe will fill the reservoir in 20 hrs.