# 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 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 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 ( : ).

Sub-duplicate ratio of (a : b) is (a : b).

Triplicate ratio of (a : b) is : )..

Sub-triplicate 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 ∞