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 cheaper
    C.P. of a unit quantity
    of dearer
    (c) Mean Price
    (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.