Ratio and Proportion
About 6 min · Numerical and Mathematical Ability · English
Time worked out from the lesson's 328 words at 150 words a minute, plus a minute for each question.
The topic tests your ability to compare quantities, scale them proportionally, and solve real-world problems involving partnerships and resource distribution. Mastering this area is essential because ratio concepts underpin several other topics like percentage, mixture problems, time-work relationships, and profit-loss calculations.
Key ideas
- Ratio expresses how many times one quantity contains another. Written as a:b, it means for every 'a' units of the first quantity, there are 'b' units of the second. Ratios are fractions in disguise: a:b = a/b.
- Proportion states that two ratios are equal: a:b = c:d, or equivalently a/b = c/d. Cross-multiplication gives ad = bc, the fundamental property used to solve proportion problems.
- Direct Proportion: When one quantity increases, the other increases proportionally (y = kx). Example: more workers complete more work in the same time.
- Inverse Proportion: When one quantity increases, the other decreases proportionally (xy = k). Example: more workers complete the same work in less time.
- Compound Ratio: The ratio obtained by multiplying corresponding terms of two or more ratios. If ratios are a:b and c:d, the compound ratio is ac:bd. Used when multiple factors affect a comparison simultaneously.
Quick reference
- Ratio a:b means a/b. To find actual values from ratio and sum, use [a/(a+b)]×Sum.
- Proportion a:b = c:d gives ad = bc. Use cross-multiplication to solve for unknowns.
- Compound ratio of a:b and c:d is ac:bd. Multiply numerators, multiply denominators.
- Partnership profit = (Capital × Time) ratio. Same time → use capital ratio; same capital → use time ratio.
- Direct proportion: y₁/x₁ = y₂/x₂. Inverse proportion: x₁y₁ = x₂y₂.
Check yourself: 3 questions
1. Two numbers are in the ratio 3:5. If 9 is added to each number, the new ratio becomes 12:17. What is the smaller number?
2. If A:B = 2:3 and B:C = 4:5, what is A:B:C?
3. The ratio of ages of Ram and Shyam is 3:5. After 6 years, the ratio will become 2:3. What is Ram's present age?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 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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