Quantitative Aptitude - Ratio & Proportions - Formula & Concepts Tutorial

1. Ratio

The ratio of two quantities a and b in the same units, is the fraction a/b and we write it as a:b .

Example

Ratio  4:8 can be represented as  .

2. Proportion

The equality of two ratios is called proportion.

If a : b = c : d , we write it as a : b :: c : d , and we say that a, b, c and d are in proportion.

Thus a : b :: c : d => (b * c) = (a * d)

A] Fourth Proportional – If a : b = c : d , then d is called the fourth proportional to a, b, c.

B] Third Proportional  - If a : b = b : c , then c is called the third proportional to a and b.

C] Mean Proportional – Mean proportional between a and b is  .

3. Compound Ratio

The Compound Ratio of the ratios (a : b), (c : d), (e : f) is (ace : bdf)

4. A] Duplicate Ratio of (a : b) is (a² : b²)

B] Sub-Duplicate Ratio of (a : b) is

C] Triplicate Ratio of (a : b) is (a³ : b³)

D] Subtriplicate Ratio of (a : b) = (a^1/3 : b^1/3)

E] Componendo and Dividendo  If   then    

5.  If a, b and c are such that a:b = b:c then a, b and c are said to be in continued proportion.