Pipes And Cisterns | Quantitative Aptitude

The problems of pipes and cisterns usually have two kinds of pipes, Inlet pipe and Outlet pipe / Leak.

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 a cistern or a reservoir, emptying it, is known as an outlet.

1. If a pipe can fill a tank in x hours, then :

Part filled in 1 hour = 1/x

For example, if a pipe takes 6 hours to fill a tank completely, say of 12 liters, then in 1 hour, it will fill 1 / 6 th of the tank, i.e., 2 liters.

2. If a pipes can empty a full tank in y hours, then :

Part emptied in 1 hour = 1/y.

For example, if a pipe takes 6 hours to empty a tank completely, say of 18 liters, then in 1 hour, it will empty 1 / 6 th of the tank, i.e., 3 liters.

3. If a pipe can fill a tank in xx hours and another pipe can fill it in yy hours, then both the pipes together can fill the tank in xy / x+y hours.

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, 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, the net part emptied

In 1 hour = (1/y - 1/x).

6. If we have a number of pipes such that some fill the tank and some empty it, and we open all of them together, then in one hour, part of the tank filled/emptied = ∑ (1 / mi) – ∑ (1 / nj), where ‘mi‘ is the time taken by inlet pipe ‘i’ to fill the tank completely if only it were open and ‘nj‘ is the time taken by outlet pipe ‘j’ to empty the tank completely if only it were open. If the sign of this equation is positive, the tank would be filled and if the sign is negative, the tank would be emptied.

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