SSC CGL · Bite-size lessons

Ratio and Proportion

About 6 min · Quantitative Aptitude · English

Time worked out from the lesson's 398 words at 150 words a minute, plus a minute for each question.

Ratio and Proportion forms the backbone of many SSC CGL quantitative aptitude problems. A firm grasp of ratio manipulation, proportion solving, and compound ratio concepts is essential.

Key ideas

• Ratio expresses the relationship between two quantities of the same kind as a quotient a:b = a/b. Ratios are unitless; 2 kg : 4 kg simplifies to 1:2.
• Proportion states that two ratios are equal: a:b = c:d or a/b = c/d. In a proportion, the product of extremes equals the product of means: a × d = b × c.
• Compound ratio is the ratio of products of corresponding terms from two or more ratios. If ratio of A to B is m:n and B to C is p:q, their compound ratio is (m×p):(n×q), which equals A:C (the three-term A:B:C is a continued ratio, found by making B equal). For two ratios a:b and c:d, compound ratio is (a×c):(b×d).
• Direct proportion: when one quantity increases, the other increases proportionally (x₁/y₁ = x₂/y₂). Inverse proportion: when one increases, the other decreases (x₁ × y₁ = x₂ × y₂).
• Duplicate ratio of a:b is a²:b². Triplicate ratio is a³:b³. Sub-duplicate is √a:√b. These appear in geometry and area/volume comparisons.

Watch out for

• Mixing ratios without equalizing common terms → When combining A:B and B:C, students forget to make B equal in both. Always find LCM of the common term's values and scale both ratios accordingly.
• Forgetting time factor in partnership → Students divide profit only by capital invested, ignoring duration. Always multiply capital by time period (months/years) before finding the ratio.
• Confusing direct and inverse proportion → Using x₁/y₁ = x₂/y₂ for inverse relationships (like more workers, less time). Remember: inverse means x₁×y₁ = x₂×y₂.

Quick reference

• Cross-multiplication: a:b = c:d ⇒ ad = bc (fastest solution method)
• Combining ratios: Equalize common term by LCM, then merge
• Partnership profit = (Capital × Time) ratio
• Fourth proportional to a,b,c = (b×c)/a
• Split total T in ratio m:n → Parts are mT/(m+n) and nT/(m+n)

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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