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Ratio and Proportion - Important Formulas |Aptitude

  1. Ratio:
    The ratio of two quantities a and b in the same units, is the fraction  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.
    Eg. The ratio 5 : 9 represents5with antecedent = 5, consequent = 9.
    9
    Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.
    Eg. 4 : 5 = 8 : 10 = 12 : 15. Also, 4 : 6 = 2 : 3.
  2. Proportion:
    The equality of two ratios is called proportion.
    If a : 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 = Product of extremes.
    Thus, a : b :: c : d  (b x c) = (a x d).
  3. Fourth Proportional:
    If a : b = c : d, then d is called the fourth proportional to a, b, c.
    Third Proportional:
    a : b = c : d, then c is called the third proportion to a and b.
    Mean Proportional:
    Mean proportional between a and b is ab.
  4. Comparison of Ratios:
    We say that (a : b) > (c : d)     a>c.
    bd
    Compounded Ratio:
    The compounded ratio of the ratios: (a : b), (c : d), (e : f) is (ace : bdf).
  5. Duplicate Ratios:
    Duplicate ratio of (a : b) is (a2 : b2).
    Sub-duplicate ratio of (a : b) is (a : b).
    Triplicate ratio of (a : b) is (a3 : b3).
    Sub-triplicate ratio of (a : b) is (a1/3 : b1/3).
    Ifa=c, thena + b=c + d.     [componendo and dividendo]
    bda - bc - d
  6. Variations:
    We say that x is directly proportional to y, if x = ky for some constant k and we write, x  y.
    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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