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    Ratio and Proportion: Formulas and Shortcuts

    Learn shortcut methods of calculating Ratio and proportion which is one of the easiest concepts from competitive exam perspective. Questions from this concept are mostly asked in conjunction with other concepts like Mixtures and Alligations. Here, you will get to know the shortcuts and formulae to solve these questions quickly and with accuracy.
    Created On: Dec 20, 2017 15:06 IST
    Modified On: Jan 24, 2018 18:40 IST
     

     

    Ratio and Proportion is one of the easiest concepts from competitive exam perspective. Questions from this concept are mostly asked in conjunction with other concepts like ‘Mixtures & Alligations’.

    Ratio and Proportion

    Learn the formulas and shortcuts of Mixture and Alligation

    RATIOS

    Ratio of two quantities a and b in same units is the fraction of the two quantitiesRatio and Proportionand is written as

    Ratio and Proportion

    Where a is called as the antecedent and b is called as the consequent.

     

    COMPARISON OF RATIOS

    Ratios can be compared. When it is said that a: b > c: d, then it means,

    Ratio and Proportion

    DIFFERENT TYPES OF RATIOS

     Ratio Table

     

    PROPERTIES OF RATIO

    If both antecedent and consequent are multiplied or divided by the same number the ratio remains unchanged.

    Ratio of two fractions can be expressed in fraction as follows:

     Ratio and Proportion

    If a: b :: c: d= n, where n is a constant then,

    Ratio and Proportion

    Ifa/A, b/B, c/C are unequal fractions then their ratio

    Ratio and Proportion

    lies between the lowest and highest fraction.

     

    If two different numbers (c and d) are to be added to the antecedent (a) and consequent (b), then it must be satisfy the following condition:

    Ratio and Proportion

    For example, if Ratio and Proportionand if 3 and 5 are to be added to the numerator and denominator respectively, then it follows as:

    Ratio and Proportion

    where

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    PROPORTION

    Proportion is the equality of two fractions, that is a: b = c: d. This can be represented as a: b :: c: d,

    Where a and d are called extremes and b and c are called the mean of the ratio.

     

    FOURTH, THIRD AND MEAN PROPORTIONS

    In a : b :: c : d, d is the fourth proportion of a, b and c; and c is the third proportion of a and b.

    The mean proportion of a and b is Ratio and Proportion

     

    DIFFERENT FORMS OF PROPORTION

     Proportion Table

     

    PROPERTIES OF PROPORTION

    Product of extremes is equal to the product of means.

    If a: b :: b: c, then

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    If three quantities are in proportion as in a: b :: b: c, then,

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    where b is the mean proportion to a and b. c is the third proportion to a and b.

     

    If three quantities are in proportion as in a: b :: b: c, then,

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