Numerical Applications
Mixtures and Alligation:-
- When two or more substances are mixed together, they form a Mixture.
- The method to find out the quantity of each substance in a mixture is called Alligation.
Let us mix two ingredients A and B to form a mixture X. Let the quantities of A and B be a and b and the cost price per unit be C1 and C2 respectively.
The per unit price of the mixture X is Cm.
Then, the cost price of mixture X = Cost price of ingredient A + Cost price of ingredient B
From (1), we get
This shows that Cm is the weighted mean of cost price C1 and C2 of ingredients A and B respectively.
So, Cm lies between C1 and C2. Suppose then C1 < Cm < C2
Also, from (2), we get
Alligation grid:-
The result of (2), can be represented using the alligation grid:-
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