# Quantitative Aptitude - Ratio & Proportions - Formula & Concepts Tutorial

**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 .

**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 .

**Compound Ratio**

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

**A] Duplicate Ratio**of (a : b) is (a^{2}: b^{2})

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

**C] Triplicate Ratio** of (a : b) is (a^{3} : b^{3})

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

**E] Componendo and Dividendo** If then

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