Ratio and Proportion - Quantitative Aptitude - Aptitude question and answers

Explanation / Important formulas:

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.
  • Example: 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.]

Example:  4 : 5 = 8 : 10 = 12 : 15. Also, 4 : 6 = 2 : 3.

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).

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.

Comparison of Ratios: We say that (a : b) > (c : d) <=> a / b > c / d

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

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/b = c/d, then a + b / a – b =c + d / c – d [Componendo and dividendo]

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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Ratio and proportion - Question and Answers

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