Ratio and Proportion
About 6 min · Quantitative Ability · 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 a foundational pillar of quantitative ability in HSSC CET. Mastering this topic gives you a reliable scoring opportunity with minimal calculation.
Key ideas
- Ratio is a comparison of two quantities by division, written as a : b or a/b. Both quantities must be in the same unit. A ratio has no unit itself.
- Proportion means two ratios are equal: if a : b = c : d, then a, b, c, d are in proportion. Here, a and d are called extremes, while b and c are called means.
- Product rule of proportion: In a proportion a : b :: c : d, the product of extremes equals the product of means, i.e., a × d = b × c.
- Types of proportion: Direct proportion (both quantities increase/decrease together), Inverse proportion (one increases as the other decreases).
- Third proportional: If a : b = b : c, then c is the third proportional to a and b. Formula: c = b²/a.
Watch out for
- Wrong thinking: Adding ratios instead of multiplying for partnership. Correct fix: Always multiply Capital × Time for each partner before finding the ratio.
- Wrong thinking: Forgetting to convert quantities to the same unit before forming a ratio. Correct fix: Always ensure both quantities are in identical units (both in kg, both in cm, etc.) before dividing.
- Wrong thinking: Simplifying ratios incorrectly by subtracting instead of dividing. Correct fix: To simplify 15 : 25, divide both by HCF (5) to get 3 : 5. Never subtract.
Quick reference
- Ratio a : b means for every 'a' units of first, there are 'b' units of second.
- Proportion check: Cross-multiply — if products are equal, the ratios are in proportion.
- To divide amount X in ratio a : b: A gets X × a/(a+b), B gets X × b/(a+b).
- Mean proportional of a and b = √(ab).
- Partnership rule: Profit share ∝ Capital × Time.
Check yourself: 3 questions
1. A sum of Rs 7700 is to be divided among A, B and C in the ratio 2:3:6. How much money will B receive?
2. The ratio of the ages of A and B is 5:7. After 6 years, the ratio of their ages will be 3:4. What is the present age of A?
3. If A:B = 2:3 and B:C = 4:5, then what is A:C?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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