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Home->Aptitude->Ratio and Proportion -> Important Formulas

Ratio and Proportion :-

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IMPORTANT EXAMPLES
::Important Formulas

Here Some Basic Formulas/Rules Are given below :-

  1. RATIO : The ratio of two quantities a and b in the same units, is the fraction a/b and we write it as a : b.
    In the ratio a: b, we call a as the first term or antecedent and b, the second term or consequent.
    Ex. The ratio 5 : 9 represents 5/9 with antecedent = 5, consequent = 9.
    Rule : The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.
    Ex. 4 : 5 = 8 : 10 = 12 : 15 etc. Also, 4 : 6 = 2 : 3.

  2. PROPORTION : The equality of two ratios is called proportion. Ifa:b=c:d, we write, a: b:: c: d and we say that a, b, c, d are in proportion. Here a and d are called extremes, while b and c are called mean terms.
    Product of means = Producut of extremes.
    Thus, a : b :: c : d <=> ( b x c ) = ( a x d ).

    1. Fourth Proportional : If a : b = c : d, then d is called the fourth proportional to a, b, c.

    2. Third Proportional : If a : b = b : c, then c is called the third proportional to a and b.

    3. Mean Proportional : Mean proportional between a and b is √ab

    1. COMPARISON OF RATIOS: We say that (a : b) > (c : d) <=> a/b > c/d

    2. COMPOUNDED RATIO: The compounded ratio of the ratios (a : b), (c : d), (e : f) is (ace : bdf).

    1. Duplicate ratio of (a : b) is (a2 : b2).

    2. Sub-duplicate ratio of (a : b) is ( √a : √b )

    3. Triplicate ratio of (a : b) is (a3 : b3).

    4. Sub-triplicate ratio of (a : b) is
      =   1   :   1  
          a3     b3

    5. If a/b = c/d then a+b/a-b = c+d/c-d

    1. VARIATION :
    2. We say that x is directly proportional to y, if x = ky for some constant k and we write, x = y.

    3. We say that x is inversely proportional to y, if xy = k for some constant k and we, write : x = 1/y

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