Complete Ratio and Proportion Forumula and Tricks for UPSC CSAT 2024 and 2025

On this page, we have compiled the complete list of short tricks and formula for CSAT questions related to Ratio and Proportion.

Ratio: Ratio is the relation that one quantity bears to another of the same kind. The comparison is made by considering what multiple or part the first quantity is of the second. Thus, the ratio of one quantity to another is measured by "a:b" or by fraction "a/b".

Proportion: If two ratios are equal, they make a proportion or, the equality of two ratios constitutes a proportion. Thus:

$$ {2 \over 3} = {4 \over 6}$$

$${2:3} :: {4:6}$$

The above is read as: 2 is to 3 as 4 is to 6.

Numbers: Ratio & Proportion Formula

If a:b::c:d, i.e. if a is to b as c is to d, then the following formulae are applicable:

$$\frac{a}{b}=\frac{c}{d}$$

$$a = \frac{b \times c}{d}$$

$$b = \frac{a \times d}{c}$$

$$c = \frac{a \times d}{b}$$

$$d = \frac{b \times c}{a}$$

In proportion, the product of extremes is always equal to the product of medians (i.e., a x d = b x c, always).

LCM, HCF: Ratio & Proportion Formula

If LCM x HCF = a x b, then:

$$\text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}}$$

$$\text{HCF of fractions} = \frac{\text{HCF of numerator}}{\text{LCM of denominator}}$$

Average: Ratio & Proportion Formula

Average: An average o a number of quantities of the same kind is their sum divided by the number of those quantities.

$$Average = \frac{\text{sum of numbers of quantities}}{\text{total number of quantities}}$$