Ratio and Proportion Formulas

1. Basic Ratio Formula

Ratio = \frac{Part 1}{Part 2}

The ratio represents the relationship between two quantities by division.

a : b :: c : d \to a \times d = b \times c

In proportion, the product of the extremes equals the product of the means.

a : b :: b : c \to b = \sqrt{a \times c}

In continued proportion, the second term is the geometric mean of the first and third terms.

Duplicate Ratio = a : b \to a^{2} : b^{2}

The duplicate ratio is obtained by squaring the terms a and b of the given ratio.

Inverse Ratio = a : b \to b : a

The inverse ratio is obtained by swapping the terms of the given ratio.

Part 1 = \frac{Ratio 1}{Sum of Ratios} \times Total Quantity

Similarly,

Part 2 = \frac{Ratio 2}{Sum of Ratios} \times Total Quantity

This formula helps to divide a quantity into parts based on a given ratio.

x \propto y \to \frac{x1}{x2} = \frac{y1}{y2}

In direct proportion, as one quantity increases, the other also increases in the same ratio.

x \propto \frac{1}{y} \to x1 \times y1 = x2 \times y2

In inverse proportion, as one quantity increases, the other decreases in such a way that their product remains constant.

Average Ratio = \frac{Sum of All Ratios}{Number of Ratios}

The average ratio is calculated by dividing the sum of all ratios by the total number of ratios.

Value of 1 Unit = \frac{Total Value}{Number of Units}

The unitary method finds the value of a single unit from the total value and the number of units.