Ratio and Proportion Formulas, Questions and Study Material
Ratio and Proportion Solved Examples  Page 2
Ratio and Proportion Online Test  Page 3
Ratio and Proportion Video Lecture  Page 4
Ratio and Proportion Formulas
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.
Example: The ratio 5 : 9 represents with antecedent = 5, consequent = 9.
Rule: The multiplication or division of each term of a ratio by the same nonzero 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 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)
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 ( : ).
Subduplicate ratio of (a : b) is (a : b).
Triplicate ratio of (a : b) is : )..
Subtriplicate ratio of (a : b) is
If , then [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 ∞
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