**Alligation** or Mixture: Alligation is an old and practical method of solving arithmetic problems related to mixtures of ingredients. There are two types of alligation: alligation medial, used to find the quantity of a mixture given the quantities of its ingredients, and alligation alternate, used to find the amount of each ingredient needed to make a mixture of a given quantity. Alligation medial is merely a matter of finding a weighted mean. Alligation alternate is more complicated and involves organizing the ingredients into high and low pairs which are then traded off.

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**What is a Mixture?**

** **A

When two varieties of rice are mixed to form a new variety of rice then it is called as a mixture.

**What is an Alligation?**

** **If two ingredients A and B of price x and y respectively are mixed and the price of the resultant mixture is M (mean price)then the ratio (R) in which ingredients are mixed is given by,

** **An

** ****Formulas for Mixtures and alligation questions **

** Example 1**:

** Step 1:** First, we need to find the price of the mixed salt, that is Profit = 25% Selling Price = 40 paise/kg Cost of the Mixture = 32 paise

** Step 2: **Use the pictorial representation method to find the ratios.

** Step 3:** The ratio = 4 : 5 Quantity(dearer) : Quantity (Cheaper) = 4 : 5

Quantity(dearer) : 25 = 4 : 5

Quantity(dearer) x 5 = 4 x 25

Quantity(dearer) = 100/5

Quantity(dearer) = 20kg

Therefore, The 20kg of dearer quantity is supposed to be mixed with 25kg of cheaper quantity to make a new mixture of salt.