## Pipes & Cisterns

Problems related to pipes & cisterns are similar to those of time and work but with a slight difference of conceptual agents like inlets & outlets.**Basic Terms:**

**Inlet:**A pipe which is used to fill up the tank,cistern or reservoir is known as 'Inlet'. This type of nature indicates 'plus' or 'positive type' of work done.

**Outlet:**A pipe which is used to empty the tank, cistern or reservoir is known as 'Outlet'. This type of nature indicates 'minus' or 'negative type' type of work done.

**Important Formulae:**

1) If a pipe requires 'x' hours to fill up the tank, then part filled in 1 hr = | 1 |

x |

2) If a pipe requires 'y' hours to empty the full tank, then part emptied in 1 hr = | 1 |

y |

3) Net Work Done = (Sum of work done by inlets) - (Sum of work done by outlets)

4) Suppose that one pipe takes 'x' hours to fill up the tank and the another pipe takes 'y' hours to empty the full tank, then, on opening both the pipes, there are 2 possible conditions:

For condition I: x < y, Net part filled in 1 hr = | 1 | – | 1 |

x | y |

For condition II: x > y, Net part emptied in 1 hr = | 1 | – | 1 |

y | x |

**Quick Tricks & Tips:**

1) If two pipes take 'x' & 'y' hrs respectively to fill the tank and the third pipe takes 'z' hrs to empty the tank and all of them are opened together, then

The net part filled in 1hr = | 1 | + | 1 | – | 1 |

x | y | z |

Hence,

The time taken to fill the tank = | 1 |

(1/x) + (1/y) + (1/z) |

2) Consider a pipe fills the tank in 'x' hrs. If there is a leakage in the bottom, the tank is filled in 'y' hrs.

If the tank is full, the time taken by the leak to empty the tank = | hrs | ||||

1 | |||||

| |||||

3) Suppose that pipe 'A' fills the tank as fast as the other pipe 'B'. If pipe 'B' (slower) & pipe 'A' (faster) take 'x' min & 'x/n' min respectively to fill up an empty tank together, then

Part of the tank filled in 1 hr = | n + 1 |

x |

**Questions Variety:**

Type 1: Find the time to fill/ empty the tank by the pipes together for the given time of individual pipes.

**Examples:**

**Q 1.**Two pipes A & B can fill the tank in 12 hours and 36 hours respectively. If both the pipes are opened simultaneously, how much time will be required to fill the tank?

a. 6 hours

b. 9 hours

c. 12 hours

d. 15 hours

View solution

Correct answer:(b)**Hint: **

If a pipe requires 'x' hrs to fill up the tank, then part filled in 1 hr = | 1 |

x |

If pipe A requires 12 hrs to fill the tank, then part filled by pipe A in 1 hr = 1/12

If pipe B requires 36 hrs to fill the tank, then part filled by pipe B 1 hr = 1/36

Hence, part filled by (A + B) together in 1 hr = 1/12 + 1/36

= 48 / 432 = 1/9

In 1 hr both pipes together fill 1/9th part of the tank. This means, together they fill the tank in 9 hrs.

**Q 2.**Two pipes can fill a tank in 6 hours and 8 hours respectively while a third pipe empties the full tank in 12 hours. If all the three pipes operate simultaneously, in how much time will the tank be filled?

a. 7(1/2) hrs

b. 4(4/5) hrs

c. 3 (2/7) hrs

d. 1(1/5) hrs

View solution

Correct answer:(b) **Hint:** If one pipe fills the tank in 'x' hrs, another pipe fills the same tank in 'y' hrs but the third pipe empties the tank in 'z' hrs and all of them are opened together, then

The net part filled in 1hr = | 1 | + | 1 | – | 1 |

x | y | z |

From the given data, net part filled in 1 hour = 1/6 + 1/8 -1/12 = 5/24

So, total time to fill the tank with all pipes open = 24/5 hrs