Ratio and Proportion Formulas, Questions and Study Material

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Ratio and Proportion Online Test - Page 3
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Ratio and Proportion Formulas

Ratio: The ratio of two quantities a and b in the same units, is the fraction $\frac{a}{b}$ 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 $\frac{5}{9}$ 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.
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 $\Leftrightarrow$ (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) $\Leftrightarrow$ $\frac{a}{b}>\frac{c}{d}$

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 ($a^{2}$ : $b^{2}$).

Sub-duplicate ratio of (a : b) is (a : b).
Triplicate ratio of (a : b) is $a^{3}$ : $b^{3}$)..
Sub-triplicate ratio of (a : b) is $a^{\frac{1}{3}}\, :\, b^{\frac{1}{3}}$
If $\frac{a}{b}\, =\frac{c}{d}$, then $\frac{a\,+\,b}{a\,-\,b}\, =\,\frac{c\,+\,d}{c\,-\,d}$ [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 ∞ $\frac{1}{y}$