Alligation alternate method:

This method was mostly used in pharma industry to find out the intermediate strength of a compound by mixing two seperate preperations which are similar and having different strengths.  This is the simplest calculation available for mixing problems. This method was also used to find out the amount of each compound required to make a mixture of given quantity.

 How much of a compound A of strength X % and the same compound A of Y % needed to make C grams of same compound A of strength Z %.

So total parts needed = (Y-Z) + (X-Z)  = B parts

So, (Y-Z)/B = M & (X-Z)/B = N

M * C grams of compound A = J grams of compound A of strength Y % was required to make C grams of compound A of strength Z %

N*C grams of compound A = K grams of compound A of strength X% was required  to make C grams of compound A of strength Z %.

You can see that, J grams + K grams = C grams of the compound A

 

You can use the alligation alternative method in a very simple form to predict solutions for mixing as given below: 

For example, if you have high grade limestone of 96% CaCO3 content and a low grade limestone of 21% CaCO3 content.But you require 81% CaCO3 content. So in what proportion you can mix these high grade and low grade limestones to get the desired 81% CaCO3 content limestone?

 

So, 60 parts of highgrade limestone to be mixed with 15 parts of lowgrade limestone to get 81% of CaCO3 content limestone.

So, highgrade limestone : low grade limestone = 60:15 = 4:1.

Hence, 4 parts of highgrade limestone to be mixed with 1 part of low grade limestone to get 81% CaCO3 content limestone.

 

Lets see another example.

 

What is the mixing proportion required to get 200 tons of 75% CaCO3 content limestone with a limestone of 90% CaCO3 content and with clayey marl of 30% CaCO3 content.

 

  

Total  parts required = 45+15 = 60 parts

So (45/60) * 200 = 150 tons of limestone was needed to produce 75% CaCO3 content. 

And (15/60) * 200 = 50 tons of clayey marl was needed to produce 75 % CaCO3 content.

So 150 tons + 50 tons = 200 tons of 75 % CaCO3 content.


You can use this alligation alternate method for all kind of mixing calculations like mixing of lime and silica or clay,any other material mixing and even mixing of liquids etc.,

Note: Always substract from higher value to lower value in this method.