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Aptitude - Ratio and Proportion

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  • Important Formulas

Exercise

"When ambition ends, happiness begins."
- (Proverb)
  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 represents 5 with 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 .
    b d

    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).

    If a = c , then a + b = c + d .     [componendo and dividendo]
    b d a - b c - 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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