In this section, the following topics are discussed with examples

**Mixtures****Alligations****Examples**

### Example 1:

**In what ratio must coffee at Rs 93 per Kg be mixed with coffee at Rs 108 per Kg so that the mixture be worth Rs 100 per Kg?**

**Sol:**

108 – 100 : 100 – 93

So, the ratio is 8 : 7 (simple as like that).

### Mixtures

Mixtures are called as a drunken concept in quants because it involves mostly with alcohol and also another reason is that it is bit tricky when comes to the part of calculations.

Final Amount of ingredient = Initial Amount x (Vol. after removal / Vol. after replacing)^{n}

## No excellent soul is exempt from a mixture of madness.

ARISTOTLE

#### Example 1

**A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 liters of the mixture is removed and replaced with pure milk and the operation is repeated once more.**

**At the end of the two removals and replacement, what is the ratio of milk and water in the resultant mixture?**

** **

**Sol:**

**Step 1:**

As per the given statement 20lts is of the ratio 3:2. so it will be having milk and water in the amount of 12 : 8

Now when you remove the 10 liters of this mixture that will also be in the ratio of 3:2 now 10 lts ratio of 3:2 is 6 lts of milk and 4 lts of water

**Step 2:**

So after removing the ratio of the new mixture will be milk : water = 6:4

Now by adding 10 lts of pure milk the ratio will become as 16:4.

**Step 3:**

Now again 10 lts of this mixture is removed for the last time now looking at the ratio the mixture should be removed in the ratio of 16:4 in the sense 4:1.

So the amount of milk and water that is removed from the given mixture is 8:2

**Step 4:**

Now the final mixture after removing will be of the amount 8 : 2

Adding 10 lts of milk again to it we arrive at the final volume 18 : 2.

.`. the final volume is given as 18 : 2.