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Mixture and Alligation: Formulas and Shortcuts

Jan 24, 2018 17:40 IST


    ‘Mixtures & Alligations’ is an integral part of Ratio and Proportion topic of Quantitative Aptitude section. In competitive exams, you will find a question asked every year from this topic and hence, it is a crucial topic from examination perspective.

    Mixture and Alligation


    When two or more components are mixed together in a certain ratio or proportion, then that composition is called a mixture.

    Mixture Maths

    Learn the formulas and shortcuts of Ratio and Proportion


    The word alligation means linking.

     Alligation Maths

    Alligation is the rule which enables us to find the ratio in which two or 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 which is denoted by (x).

    Rule of Alligation

    The rule of alligation helps us to find the mean or average value of mixture when the price of the two or more ingredients and the proportion in which they are mixed are given.

    Mathematical Formula

     Rule of Alligation Formula

     Rule of Alligation Chart 

    Therefore, (cheaper quantity): (dearer quantity) = (d-m): (m-c)

    Example: If the rice at Rs. 320 per kg and the rice at Rs. 350 per kg be mixed, then in what proportion they should be mixed so that the new mixture is worth Rs. 335 per kg?

    Solution:         Rule of Alligation Example

                               Applying rule of alligation:

                              Rule of Alligation Example

                        Hence, they must be mixed in equal proportion, i.e., 1:1.

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