TNPSC Group IV · Bite-size lessons

Ratio and Proportion

About 6 min · Aptitude and Mental Ability Test · English

Time worked out from the lesson's 345 words at 150 words a minute, plus a minute for each question.

Ratio and Proportion is a foundational topic in the TNPSC Group IV Aptitude section. This topic tests your ability to compare quantities, distribute amounts, and solve real-world problems involving mixtures, partnerships, and scaling.

Key ideas

• Ratio is a comparison of two quantities of the same unit, written as a:b or a/b. The first term (a) is the antecedent, the second (b) is the consequent.
• Proportion means two ratios are equal. If a:b = c:d, then a, b, c, d are in proportion. Here, a and d are extremes, b and c are means.
• Product of extremes = Product of means: In a:b::c:d, we have a × d = b × c. This is the fundamental rule for solving proportion problems.
• Direct Proportion: When one quantity increases, the other increases proportionally. Example: More items purchased → More money spent.
• Inverse Proportion: When one quantity increases, the other decreases proportionally. Example: More workers → Less time to complete work.

Watch out for

• Forgetting to convert units → If comparing 2 metres and 50 cm, first convert to same unit: 200 cm : 50 cm = 4:1. Always check units before forming ratios.
• Not simplifying to lowest terms → Writing 6:9 instead of 2:3. Always divide both terms by their HCF for the final answer.
• Confusing direct and inverse proportion → Thinking more workers means more days. Ask yourself: "If one increases, does the other increase (direct) or decrease (inverse)?"

Quick reference

• Ratio a:b means a/b; always simplify to lowest terms
• Proportion rule: a:b::c:d means a×d = b×c
• To divide N in ratio a:b:c → parts are Na/(a+b+c), Nb/(a+b+c), Nc/(a+b+c)
• Direct: both increase/decrease together; Inverse: one up, other down
• Compound ratio = product of antecedents : product of consequents

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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