MH Police Bharti · Bite-size lessons
Ratio & Proportion
About 6 min · Mathematics · English
Time worked out from the lesson's 323 words at 150 words a minute, plus a minute for each question.
Ratio & Proportion is a topic in Maharashtra Police Bharti mathematics section. Questions may appear in straightforward forms—comparing quantities, finding unknown values, or distributing amounts among partners. Mastering this topic also strengthens your foundation for related concepts like percentages, mixtures, and time-work problems.
Key ideas
- Ratio compares two quantities of the same unit. Written as a:b or a/b. The ratio 4:6 simplifies to 2:3 by dividing both terms by their HCF.
- Proportion states that two ratios are equal. If a:b = c:d, then a×d = b×c (cross-multiplication rule). This is called the "product of means equals product of extremes."
- Direct Proportion: When one quantity increases, the other increases proportionally. Example: More workers → more work done (in same time).
- Inverse Proportion: When one quantity increases, the other decreases proportionally. Example: More workers → less time needed (for same work).
- Compounded Ratio: When ratios a:b and c:d are compounded, result is (a×c):(b×d).
Watch out for
- Not simplifying ratios to lowest terms → Always divide both terms by HCF before proceeding. Ratio 12:18 must become 2:3.
- Confusing direct and inverse proportion → Ask: "Does increasing one quantity increase or decrease the other?" If opposite directions, it's inverse.
- Forgetting time factor in partnership → Profit sharing depends on BOTH capital AND time invested. Rs 10,000 for 6 months ≠ Rs 10,000 for 12 months.
Quick reference
- Ratio a:b means a/b; always simplify using HCF
- In proportion a:b :: c:d, cross-multiply: a×d = b×c
- Mean proportional of a and b = √(a×b)
- Direct: x increases → y increases; use x₁/y₁ = x₂/y₂
- Inverse: x increases → y decreases; use x₁×y₁ = x₂×y₂
Check yourself: 3 questions
1. Two numbers are in the ratio 3:5. If their sum is 96, find the smaller number.
2. If A:B = 2:3, B:C = 4:5 and C:D = 6:7, then find A:D.
3. Two numbers are in the ratio 3:5. If the sum of the numbers is 96, what is the smaller number?
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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