Mixtures are formed when two or more quantities of different values are mixed together.
Alligation is a practical method of solving arithmetic problems related to mixtures of ingredients. There are two kinds of problems:
- To find the quantity of a mixture given the quantities of its ingredients. (Alligation Medial)
- To find the amount of each ingredient needed to make a mixture of a given quantity. (Alligation Alternate)
Allegation: It is the rule that enables us to find the ratio in which two of more ingredients at the given price must be mixed to produce a mixture of a desired price.
Mean Price: The cost price of a unit quantity of the mixture is called the mean price.
Rule of Allegation: If two ingredients are mixed then Quantity of Cheaper / Quantity of Dearer = (C.P. of Dearer - Mean Price) / (Mean Price - C.P. of Cheaper)
Rule of Allegation: If two ingredients are mixed then Quantity of Cheaper / Quantity of Dearer = (C.P. of Dearer - Mean Price) / (Mean Price - C.P. of Cheaper)
| CP of unit quantity of cheaper (c) | CP of unit quantity of dearer (d) | |
| Mean Price (m) | ||
| d - m | (m - c) |
Cheaper quantity:Dearer quantity = (d-m):(m-c)
Suppose a container contains x units of liquid from which y units are taken out and replaced by water. After n operations the quantity of pure liquid = x (1 - y/x)n unitsNEXT
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