UP Police Constable · Bite-size lessons
Ratio and Proportion
About 5 min · Numerical & Mental Ability · English
Time worked out from the lesson's 281 words at 150 words a minute, plus a minute for each question.
Ratio and Proportion forms a fundamental pillar of the Numerical & Mental Ability section in the UP Police Constable exam. Mastery of this topic is non-negotiable because ratio problems appear both directly and embedded within other question types.
Key ideas
- Ratio is a comparison of two quantities of the same kind, written as a:b or a/b. Ratios have no units and can be simplified like fractions (12:18 = 2:3).
- Proportion states that two ratios are equal: a:b = c:d, written as a:b::c:d. In proportion, the product of extremes equals the product of means (a×d = b×c).
- Direct Proportion: When one quantity increases, the other increases proportionally (more workers → more work). If a∝b, then a₁/a₂ = b₁/b₂.
- Inverse Proportion: When one quantity increases, the other decreases proportionally (more speed → less time). If a∝1/b, then a₁/a₂ = b₂/b₁.
- Compound Ratio: The ratio compounded from two or more ratios by multiplying corresponding terms. Compound ratio of a:b and c:d is ac:bd.
Quick reference
- Ratio simplification: Divide by HCF. Always express in lowest terms.
- Proportion test: Product of extremes = Product of means (a×d = b×c).
- Direct proportion: Same direction change. Use a₁/a₂ = b₁/b₂.
- Inverse proportion: Opposite direction change. Use a₁/a₂ = b₂/b₁.
- Partnership profit ratio: (Capital₁ × Time₁) : (Capital₂ × Time₂).
Check yourself: 3 questions
1. If x varies inversely as y and x = 15 when y = 6, find the value of y when x = 18.
2. The compound ratio of (2:3), (9:4) and (5:6) is:
3. The ratio of ages of A and B is 5:7. After 6 years, the ratio will become 3:4. What is the present age of A?
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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