# Quantitative - Ratio Proportion and Variation

## Ratio Proportion and Variation Description

1. Ratio:-
• The ratio of two quantities in the same units is a fraction that one quantity is of the other.
• Thus, a to b is a ratio (a/b), written as a: b
• The first term of a ratio is called antecedent, while the second term is known as consequent. Thus, the ratio 5:8 represents 5/8 with antecedent 5 and consequent 8.
• Note:- The multiplication or division of each term of a ratio by a same non-zero number does not effect the ratio. E.g:- 3:5 is the same as 6:10 or 9:15 or 12:20.

2. Proportion:-

• The equality of two ratios is called proportion. Thus, 2:3 = 8:12 is written as 2:3::8:12 and we say that 2,3,8 and 12 are in proportion.
• The first and fourth terms are known as extremes, while second and third terms are known as Means
• Note:- Product of Means = Product of Extremes

3. Fourth Proportional:-
If a: b = c: d, then d is called the fourth proportional to a, b, c.

4. Third Proportional:-  If a: b = c: d, then c is called the third proportion to a and b.

5. Mean Proportional:- Mean proportional between a and b is ab.

6. Compounded Ratio:- The compounded ratio of the ratios: (a: b), (c: d), (e: f) is (ace: bdf)

7. Duplicate Ratios:-
• Duplicate ratio of (a: b) is (a2  : b2)
• Sub duplicate ratio of (a: b) is ${(\sqrt{a}:\sqrt{b})}$
• Triplicate ratio of (a: b) is (a3  : b3)
• Sub â€“ triplicate ratio of (a: b) is ${(a^{1/3}: b^{1/3})}$
If ${\frac{a}{b} = \frac{c}{d}}$ , then $\frac{a+b}{a-b} = \frac{c+d}{c-d}$, (Componendo and dividendo)

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