Ratio and Proportion — SSC CHSL Study Notes

Overview

Ratio and Proportion is a high-weightage arithmetic topic in SSC CHSL Tier 1, typically contributing 2–4 questions per paper. This topic forms the foundation for many other areas including percentages, partnership, mixture-allegation, and time-speed-distance problems. The exam tests your ability to manipulate ratios, solve proportion equations quickly, and apply ratio logic to real-world scenarios like profit sharing and ingredient mixing.

Students must master three core areas: basic ratio operations and compound ratios, direct/inverse/continued proportions, and partnership problems (simple and compound). The questions range from straightforward ratio simplification to multi-step word problems involving age relations, salary divisions, and business profit distribution. Speed and accuracy in cross-multiplication and ratio-chain calculations directly impact your score, making this a must-master topic for the quantitative aptitude section.

Key Concepts

• **Ratio** expresses the relationship between two quantities of the same kind as a quotient (a:b means a/b). Ratios have no units and can be simplified like fractions by dividing by the HCF of terms.

• **Proportion** states that two ratios are equal (a:b = c:d, written as a:b::c:d). In any proportion, the product of extremes equals the product of means: a×d = b×c. This cross-multiplication property solves most proportion problems.

• **Compound ratio** is formed by multiplying corresponding terms of two or more ratios. If ratios are a:b and c:d, their compound ratio is ac:bd. Used when multiple relationships combine (like combining age ratios at different times).

• **Mean proportional** between two numbers a and c is the number b such that a:b = b:c, giving b² = ac, so b = √(ac). The middle term in a continued proportion.

• **Third proportional** to a and b is the number c where a:b = b:c, making c = b²/a. The fourth term when the first two terms repeat.

• **Fourth proportional** to a, b, c is the number d where a:b = c:d, giving d = bc/a. Standard proportion completion.

• **Partnership** applies ratio principles to divide profit or loss among partners based on their capital contributions and time periods. Simple partnership considers only capital; compound partnership accounts for different time durations.

• **Direct proportion**: when one quantity increases, the other increases proportionally (y ∝ x means y/x is constant). Inverse proportion: when one increases, the other decreases (y ∝ 1/x means xy is constant).

Formulas / Key Facts

• **Ratio simplification**: Divide both terms by their HCF. Example: 45:60 = 3:4 (dividing by 15).

• **Compound ratio of a:b, c:d, e:f** = ac·e : bd·f (multiply all first terms, multiply all second terms).

• **Cross-multiplication rule**: If a:b = c:d, then ad = bc. This solves for any unknown term.