Ratio & Proportion – Notes, Rules & Examples

Ratio basics to mixtures — 13 concepts with rules, examples and common mistakes.

Quantitative Aptitude13 conceptsEnglish + हिंदी136 practice questions

Concept 1 · free preview

What is a ratio?

Understand

A ratio a : b compares two quantities of the same kind by division — a : b = a/b. Multiplying or dividing both terms by the same number does not change it.

Rule

First term = antecedent, second = consequent
Both quantities must be in the same unit; the ratio itself has no unit
Order matters: 2 : 3 ≠ 3 : 2
Simplest form: divide both terms by their HCF

Given	What to do	Example
Decimals	Multiply by 10, 100…	1.2 : 0.8 = 12 : 8 = 3 : 2
Fractions	Multiply by the LCM of the denominators	1/2 : 2/3 → × 6 → 3 : 4
Different units	Convert to one unit first	40 cm : 2 m = 40 : 200 = 1 : 5

Rule

Comparing two ratios: a : b > c : d if a × d > b × c. 3 : 5 vs 4 : 7 → 21 > 20 → 3 : 5 is larger.

Common mistake

Writing a ratio without matching units: 40 cm : 2 m is not 40 : 2 = 20 : 1.

Check yourself

Write 250 g : 1.5 kg in simplest form.

12 more concepts in this note

The k-method: think in parts
Combining ratios: A : B : C and compound ratio
Dividing an amount in a ratio
2A = 3B = 5C and ‘half / one-third’ relations
Proportion: mean, third and fourth proportional
Duplicate, triplicate and sub-ratios
What to add or subtract to make a proportion
New ratio after a change (including ages)
Income, expense and saving
Partnership: sharing profit
Coins: number ratio vs value ratio
Ratios in mixtures

Ratio & Proportion in your exam syllabus

These exams' official syllabus includes this chapter.

FAQs

What do the Ratio & Proportion notes cover?

13 concepts: What is a ratio?, The k-method: think in parts, Combining ratios: A : B : C and compound ratio, Dividing an amount in a ratio, 2A = 3B = 5C and ‘half / one-third’ relations, Proportion: mean, third and fourth proportional and more. Each concept has an explanation, rules, solved examples and common mistakes.

Are these notes available in Hindi?

Yes. Every concept is available in English and हिंदी; switch the language at the top of the note.

Are the notes free?

The first concept is free to read here. The full notes, practice questions and mock tests are part of PYQsathi Pro (₹299 per year); when a launch offer is running, its coupon is shown above and applied after you sign in. Question paper downloads are always free.

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