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# Quantitative Aptitude :: Ratio & Proportion

Home > Quantitative Aptitude > Ratio & Proportion > Important Formulas

## Ratio & Proportion Important Formulas

1. Ratio:

The ratio of two quantities of the same kind and in the same unit is a comparison by division of the measure of two quantities.
It determines how many times one quantity is greater or lesser than the other quantity.

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.

Ex. The ratio 4 : 9 represents $$\frac{4}{9}$$ with antecedent = 4, 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. 2 : 7 = 4 : 14 = 8 : 56. Also, 9 : 27 = 1 : 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 $$\Leftrightarrow$$ (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 $$\sqrt{ab}$$.

4. 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).

5. Duplicate Ratios:

Duplicate ratio of (a : b) is ($$a^{2}$$ : $$b^{2}$$).

Sub-duplicate ratio of (a : b) is ($$\sqrt{a}$$ : $$\sqrt{b}$$).

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]

6. Variations:

We say that x is directly proportional to y, if x = ky for some constant k and we write, $$x \ \alpha \ y$$ .

We say that x is inversely proportional to y, if xy = k for some constant k and
we write, $$x \ \alpha \ \frac{1}{y}$$ 