Tips and Tricks to solve aptitude problems on Mixtures and 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
    (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.


1. Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:

2. A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?

3. A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?

4. In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?

5.How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?

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