# Pipes and Cisterns Aptitude Formulas, Definitions, & Examples:

#### Overview:

 Topic Included: Formulas, Definitions & Exmaples. Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Time and Work Aptitude Notes & Questions. Questions for practice: 10 Questions & Answers with Solutions.

#### Pipe:

A pipe is a tubular section or hollow cylinder used to fill or empty the cistern or Tank.

#### Inlet Pipe:

It is a pipe that allows a liquid to enter the tank or cistern.

#### Outlet Pipe:

It is a pipe that allows a liquid to withdraw from the tank or cistern.

#### Pipes and Cisterns Case (1):

If an inlet pipe can fill a tank in $$x$$ hours, then a certain part of the tank can fill the inlet pipe in one hour = $$\frac{1}{x}$$

#### Pipes and Cisterns Case (2):

If an outlet pipe can empty a tank in $$y$$ hours, then a certain part of the tank can empty the outlet pipe in one hour = $$\frac{1}{y}$$

#### Pipes and Cisterns Case (3):

If an inlet pipe is filling the tank and an outlet pipe is emptying the tank at the same time, then a certain part of the tank can fill the inlet pipe in one hour = $$\frac{1}{x} - \frac{1}{y}$$

Example: A inlet pipe can fill a tank in two hours and a outlet pipe can empty the tank in four hours, then find the required time to fill the tank if both the pipes are running simultaneously?

Solution: Given, $$x = 2 \ hours$$, $$y = 4 \ hours$$, then a certain part of the tank filled in one hour $$= \frac{1}{x} - \frac{1}{y}$$ $$= \frac{1}{2} - \frac{1}{4}$$ $$= \frac{1}{4}$$ Hence, tank will be filled in $$4$$ hours.

#### Pipes and Cisterns Case (4):

If there are $$n$$ inlet pipes filling the tank and $$n$$ outlet pipes are emptying the tank at the same time, then a certain part of the tank can fill the inlet pipes in one hour $$= \left[\frac{1}{x_1} + \frac{1}{x_2}...\right] - \left[\frac{1}{y_1} + \frac{1}{y_2}...\right]$$

Example: Two inlet pipes can fill a tank in $$5$$ and $$10$$ hours respectively and two outlet pipes can empty the tank in $$15$$ and $$20$$ hours, then find the required time to fill the tank if all four pipes are running simultaneously?

Solution: Given, $$x_1 = 5 \ hours$$, $$x_2 = 10 \ hours$$, $$y_1 = 15 \ hours$$, and $$y_2 = 20 \ hours$$ then a certain part of the tank filled in one hour $$= \left[\frac{1}{x_1} + \frac{1}{x_2}\right] - \left[\frac{1}{y_1} + \frac{1}{y_2}\right]$$ $$= \left[\frac{1}{5} + \frac{1}{10}\right] - \left[\frac{1}{15} + \frac{1}{20}\right]$$ $$= \frac{3}{10} - \frac{7}{60}$$ $$= \frac{11}{60}$$ Hence, tank will be filled in $$\frac{60}{11}$$ hours or $$5.45$$ hours.