Alligation or Mixture - Important Formulae

1. Alligation:
   It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of desired price.
2. Mean Price:
   The cost of a unit quantity of the mixture is called the mean price.
3. Rule of Alligation:
   If two ingredients are mixed, then

   		Quantity of cheaper		=		C.P. of dearer - Mean Price
   		Quantity of dearer				Mean price - C.P. of cheaper

   We present as under:

   C.P. of a unit quantity of cheaperC.P. of a unit quantity of dearer
   (c)	Mean Price (m)	(d)
   (d - m)		(m - c)

    (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c).
4. Suppose a container contains x of liquid from which y units are taken out and replaced by water.

   After n operations, the quantity of pure liquid =		x		1 -	y		n		units.
   					x

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