Imagine you have a big tank on the roof of your house that holds 1000 liters of water. This tank helps you get water for your kitchen and other things you do every day. The water comes from the water company on the ground floor, but there's no machine to bring the water up to your tank. So, you have to fill up a bucket with water and carry it upstairs to fill the tank. Sometimes, while carrying the water, some of it spills or leaks out of the bucket.

One day, something magical happens! You get a new pipe that brings water directly from the water company to your tank.

Let us summarize things in terms of Pipes and Cisterns Problem

**Terrace water Tank: **Tank / Cisterns
**Magic Pipe : **Inlet Pipe/Tap
**Water supply in Bath, Kitchen etc: **Outlet Pipe/Tap
**Bucket/Tank leakage:** Leakage in Tank

Now that we have learned the meaning of the key terms in pipes and cisterns, let's dive into the blog to understand how pipes and cisterns work. We will also solve related problems that will help us enhance our math skills.

A pipe is a long, narrow tube that can be used to carry water or other fluids. A cistern is a large tank or reservoir that stores water. Pipes and cisterns are often used together to provide a reliable source of water. You might ask questions about how long it takes to fill or empty a tank, how much work is involved, and other similar inquiries. A studentÂ should be aware of two key things regarding such questions:

An inlet is a pipe that is connected to a tank to fill it with water. It's like a door that lets water enter. Just like when you pour water into a glass through a small hole at the top, the hole is like an inlet for the glass. In the same way, an inlet in pipes and cisterns lets water flow into them, so they can get filled up with water.

An outlet in pipes and cisterns is like a little hole or opening that allows water or liquid to flow out. Imagine you have a container filled with water, and you want the water to come out. The outlet is the place where the water comes out from the container. It may also be referred to as "leak."

We will be using a simple LCM method to solve these problems. If we find the LCM of numbers, it means we have already solved about 70% of the problem.

Let us look at simple LCM examples first before looking at actual problems:

**Example 1:**

Calculate LCM of 20, 30,10

This is a conventional method and we will keep dividing numbers till we get either 1 or all prime numbers.

LCM = 2 * 5 * 2* 3* 1= 60

- Find greatest number from list for which LCM is to be identified.
- Now look at table of this number and keep checking whether that number is divisible by other numbers in list.
- Here largest number is 30. So we will write tables of 30 and table of 20, 10 as well. We will write 30 table till we get the number which is completely divisible by 10 and 20.

- As you can see 30 is divisible by 10 but not by 20.
- However 60 is divisible by 10 and 20 both.
- So 60 is LCM [you can do this calculation orally in fraction of seconds if tables are learned 1 to 30]

Type | Given | To Find |

Type 1 | Pipe A fills tank in x hours Pipe B fills tanks n y hours | Together A & B will fill tank in how much time |

Type 2 | Pipe A fills tank in x hours Pipe B empties tank n y hours | Together A & B will fill tank in how much time tank will be filled |

Type 3 | Pipe A fills tank in x hours Due to leak it takes more time | How much time will be required to empty tank completely |

Type 4 | Miscellaneous | Miscellaneous |

**Problem 1:**

Pipe A fills tank in 10 hours and Pipe B fills tank in 15 hours. In how much time tank will fill completely if both pipes are opened together?

**Solution **

Pipe A takes 10 hours to fill tank Pipe B takes 15 hours to fill tank

First we will try to calculate what is capacity of tank in liters: which is nothing but LCM Calculate LCM of 10,15 -> LCM of 10 and 15 is 30.

So A fills 3 liters in 1 hour and 2 liters in 1 hour

In order to fill complete tank [**30 Liters]**:
1 hr Speed for Pipe A + B = 3 + 2 = 5
Time required to fill complete tank = 30 / 5 = 6 Hours
**Answer is 6 Hours**

**Problem 1:**

A Cistern can be filled by tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously then after how much time will cistern get filled?

**Solution :**

Pipe A takes 4 hours to fill tank. Pipe B takes 9 hours to fill tank

**We need to use minus sign in spped of B as it is outlet pipe.**

Calculate LCM of 4, 9 -> LCM of 4, 9 is 36.

So Cistern capacity is 36 Liters.

As you can see 1st pipe is filling tank and 2nd pipe is outlet pipe so we are using minus sign for 2nd pipe

In 1 hr total speed is 5

To fill complete tank that is 36 Litres.

36/5 = 7(1/5)

1/5 means 60/5 = 12 Minutes

**Answer is 7.2 Hours or 7 Hours 12 minutes**

**Problem 1:**

An electric pump can fill tank in 3 hours. Because of leak in the tank, it took 3(1/2) hoursto fill. If tank is full, how much time it wil leak take to empty it.

**Solution:**

Pipe A takes 3 hours to fill tank.

Pipe A with leakage (Assume leakage as B) takes 3(1/2) hours = 7(1/2)

- Here we need to find how much time leakage will require to empty completely filled pipe.
- Let us calculate LCM of 3 and 7/2
- As it sometimes become challenging to find LCM of fraction, let us see simple method
- Multiply both number for which LCM to be find.
- After that multiplication contains fraction multiply same with denominator to get natural number.
- 3* (7/2) = 21/2
- Here we have denominator and we cant take it as LCM.
- 21/2*2 = 21

**LCM of 3 and 7/2 is 21**

Now let us use same method what we used earlier: Please note that B is leakage pipe so it will have minus sign

Speed of A : 7

Speed of A with Leakage B : 6

So speed of Leakage B is 1

In order to empty filled pipe leakage will need 21 /1 = 21 Hours

**Answer is 21 Hours**

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