Ratio and Proportion

General Questions of Ratio and Proportion Problems : Level 02. Learn to solve the tricky questions based on ratio and proportion.

Ratio and Proportion Formula

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 = 9.9Rule: 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.

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 the fourth proportional to a, b, c. Third Proportional: a : b = c : d, then c is 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 (a^1/3 : b^1/3) . 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

Ratio and Proportion Questions

[WpProQuiz 147]