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Ratio and Proportion

About 6 min · Mathematics · English

Time worked out from the lesson's 416 words at 150 words a minute, plus a minute for each question.

Ratio and Proportion forms a foundational pillar of quantitative aptitude in MPESB exams. Mastering it gives you a toolkit that speeds up seemingly unrelated calculations.

Key ideas

• Ratio compares two quantities of the same unit. If A:B = 3:5, it means for every 3 parts of A, there are 5 parts of B. The actual values could be 6 and 10, or 300 and 500—the ratio remains unchanged.
• Proportion states that two ratios are equal. If A:B = C:D, then A, B, C, D are in proportion. The middle terms (B and C) are called means; the outer terms (A and D) are called extremes.
• Direct Proportion: When one quantity increases, the other increases at the same rate. Example: More workers → more output (if efficiency is constant). Mathematically, x/y = constant.
• Inverse Proportion: When one quantity increases, the other decreases proportionally. Example: More workers → less time to finish the same work. Mathematically, x × y = constant.
• Compound Ratio: Multiply corresponding terms of two or more ratios. If ratios are a:b and c:d, the compound ratio is ac:bd.

Watch out for

• Confusing direct and inverse proportion → Before calculating, ask: "If one goes up, does the other go up or down?" Up-up or down-down means direct. Up-down or down-up means inverse.
• Forgetting to make the common term equal when linking ratios → If A:B = 2:3 and B:C = 4:5, you cannot simply write A:B:C = 2:3:5. You must equalize B first using LCM.
• Adding ratios instead of multiplying for compound ratio → Compound ratio of 2:3 and 4:5 is 8:15, not 6:8. Always multiply corresponding terms.

Quick reference

• Ratio = parts, not actuals. 3:5 means 3 parts and 5 parts; use k to find values.
• Direct: same direction → x/y = constant. Inverse: opposite direction → xy = constant.
• Compound ratio: multiply across (a:b) × (c:d) = ac:bd.
• Link ratios via LCM of the common term.
• Mean × Mean = Extreme × Extreme (product rule for proportion).

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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