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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
Cma+b=C1a+C2b      ...1             Total quantity of mixture X=a+bab=C2-CmCm-C1        ...2
From (1), we get
This shows that Cm is the weighted mean of cost price C1 and C2 of ingredients A and respectively.
So, Cm lies between C1 and C2. Suppose C1<C2 then C1 < CC2
Also, from (2), we get

Quantity of cheaper ingredient AQuantity of dearer ingredient B= Cost price of dearer ingredient C2-Mean cost price CmMean cost price Cm-Cost price of cheaper ingredient C1

Alligation grid:-
The result of (2), can be represented using the alligation grid:-


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