RRB Group D · Bite-size lessons
Ratio and Proportion
About 6 min · Mathematics · English
Time worked out from the lesson's 402 words at 150 words a minute, plus a minute for each question.
It forms the backbone for solving problems in partnership, mixing solutions, time-work relationships, and even profit-loss scenarios. The exam tests your ability to quickly set up ratio equations, manipulate them algebraically, and apply them to word problems involving money distribution, ingredient mixing, or proportional division of quantities.
Key ideas
- Ratio expresses the relationship between two quantities of the same kind as a:b or a/b. A ratio of 3:4 means the first quantity is 3 parts for every 4 parts of the second. Ratios have no units and can be simplified like fractions.
- 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. This cross-multiplication property solves most proportion problems in one step.
- Compound ratio is the ratio of products of corresponding terms from two or more ratios. The compound ratio of a:b and c:d is (a×c):(b×d). If ratios are 2:3 and 4:5, compound ratio is (2×4):(3×5) = 8:15.
- Direct proportion (x ∝ y) means if one quantity doubles, the other doubles too. Cost ∝ quantity purchased. Use the relationship x₁/y₁ = x₂/y₂ to solve.
- Inverse proportion (x ∝ 1/y) means if one quantity doubles, the other halves. Workers ∝ 1/time to complete work. Use x₁×y₁ = x₂×y₂.
Quick reference
- Ratio a:b in fraction form = a/b. Always simplify by dividing by HCF.
- Four numbers in proportion when a×d = b×c (extremes product = means product).
- Compound ratio of multiple ratios = multiply all first terms : multiply all second terms.
- Partnership profit ratio = (Capital₁ × Time₁):(Capital₂ × Time₂):...
- Direct proportion: Both quantities move together. Use x₁/y₁ = x₂/y₂.
Check yourself: 3 questions
1. If A : B = 3 : 4 and B : C = 5 : 6, then what is A : B : C?
2. Three partners A, B and C invest Rs. 20,000, Rs. 25,000 and Rs. 30,000 respectively in a business. After one year, the profit is Rs. 15,000. What is the share of B in the profit?
3. The ratio of the ages of a father and his son is 7 : 3. After 10 years, the ratio will be 9 : 5. What is the present age of the son?
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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