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. |

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

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

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

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 = \(\frac{1}{x}\)

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 = \(\frac{1}{y}\)

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.

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.

Lec 1: Time and Work Case (1) and Case (2)
Exercise-1
Lec 2: Time and Work Case (3) and Case (4)
Exercise-2
Lec 3: Concept of Positive and Negative work
Exercise-3
Lec 4: Concept of Pipes and Cisterns
Exercise-4
Lec 5: Concept of Efficiency
Exercise-5