**Mixture & Allegation**

**In this Article we will going to see how to solve the Mixture & Allegation Problem as easily.**

Mixture is a fairly basic concept in Arithmetic and it is also useful and solving the problem in Averages and Percentages.

**Why this Article ?**So basically, if you take any book and go to the mixture section, we almost always see, they tends to solve the problem using complex equation and fairly complex Algebra.

Which is not really required, so now what we are going to see is how to solve the problem very easily with the pictorial representation of the problem.

So basically we will showing you a Trick, through you cal solve most of the problem very easily.

So we are starting with basic.

**What is mixture**, Mixture is basically mix two or that matter you can mix more than two things.

You can mix Pure Ingredients or you can mix two or more mixture,

For example, you can mix Alcohol and water, so here water and alcohol is a pure component. Or

You can mix mixture for that you can mix 30% alcohol drink and 50% alcohol, in 1st 30% alcohol, there 30 alcohol and 70 water and other 50% alcohol 50 alcohol & 50 water, and then you can mix this two mixtures. So this mixture will give you 100 ml of 1st mixture which contain 30 Alcohol and 70 water and 100 ml of 2nd mixture will give you 100 Alcohol and 100 water. So total we have 130 alcohol and 170 water.

We will see it in example.

100 ml 200 ml

30% Alcohol 50% Alcohol

Here is 30 Alcohol + 70 Water Here 50 Alcohol + 50 Water.

Here 30% of 100 gives 30 Alcohol & 70 Water 50% of 200 gives 100 Alcohol & 100 water.

So the total gives 130 Alcohol + 170 Water

So this could be

**130 / (130+170) = 130 / 300 = 43.34%**

**So this is have the mixtures are made and this is basic calculations in mixture so any mixture problem for that matter can be solve by doing this .**

So the main component in the mixture are Solute, most of the time are Alcohol, Sugar, Salt or any and the other one is called Solvent which is most of the time water. So any mixture problem can be solve by getting the value in the Solute in that solution or that mixture and then you get this for the other mixture and then you add the solvent and you make it the Solute is Numerator and Solvent is Denominator is Solute + Solvent ,

Solute / (Solute + Solvent) , so what we usually do.

We can do it in Different Way, it look some kind Difficult.

**This method can be solve the problem in the cross way.**

**There will be two quantities are given with there cost price, Suppose A & B and mean price or total mix price are given consider X.**

1. First we have to write the Both given Cost of quantity like A & B is shown in fig.

2. After that write the Mean or mix price at Center as shown in finger. Then draw the two cross line as shown in figure.

3. After that Minus the X value from A and write it in the cross Right Direction. It will (A - X)

4. Same as Minus the X value from B also and write it in the Cross Left Direction. It will (B - X)

**Problem 1**: In what ratio must rice at Rs. 9.30 kg per kg be mixed with rice at 10.80 per kg so that the mixer be worth Rs. 10 per kg ?

**Solution**: We are solving this problem by the new method.

We are removing this Decimal point and writing in the Kg form.

So Here is the Answer in the ratio of 80 : 70

We can write it in the simplify form = 8 : 7

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