# Pipes and Cistern Questions

**FACTS AND FORMULAE FOR PIPES AND CISTERN QUESTIONS**

**1. Inlet :** A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.

**2. ****Outlet :** A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.

**(i)** If a pipe can fill a tank in x hours, then:

part filled in 1 hour = 1/x

**(ii)** If a pipe can empty a tank in y hours, then:

part emptied in 1 hour = 1/y

**(iii)** 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, then the net part filled in 1 hour =

**(iv)** 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 =

A) 10 min. 20 sec. | B) 11 min. 45 sec. |

C) 12 min. 30 sec. | D) 14 min. 40 sec. |

Explanation:

Part filled in 4 minutes =

Remaining part =

Part filled by B in 1 minute =

The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec

A) 10 | B) 12 |

C) 14 | D) 16 |

Explanation:

Part filled in 2 hours =

Remaining part =

(A + B)'s 7 hour's work =

(A + B)'s 1 hour's work =

C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }

=

C alone can fill the tank in 14 hours.

A) 7 hours | B) 8 hours |

C) 12 hours | D) 14 hours |

Explanation:

Work done by the leak in 1 hour =

Leak will empty the tank in 14 hrs

A) 50 m^3/min | B) 60 m^3/min |

C) 72 m^3/min | D) None of these |

Explanation:

Let the filling capacity of the pump be x /min.

Then, emptying capacity of the pump=(x+10) /min.

so,

A) 3 hrs 15 min | B) 3 hrs 45 min |

C) 4 hrs 15 min | D) 4 hrs 1 |

Explanation:

Time taken by one tap to fill **half of the tank** = 3 hrs.

Part filled by the four taps in 1 hour =

Remaining part =

So, total time taken = 3 hrs. 45 mins.