Tips and Tricks on Alligation

  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
    A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
    A.
    1
    3
    B.
    1
    4
    C.
    1
    5
    D.
    1
    7

    Answer: Option C

    Explanation:

    Suppose the vessel initially contains 8 litres of liquid.

    Let x litres of this liquid be replaced with water.

    Quantity of water in new mixture = 3 – 3x x litres
    8
    Quantity of syrup in new mixture = 5 – 5x litres
    8
    3 – 3x x = 5 – 5x
    8 8

     5x + 24 = 40 – 5x

     10x = 16

     x = 8 .
    5
    So, part of the mixture replaced = 8 x 1 = 1 .
    5 8 51
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