Ratio & Proportion — Compare and Scale

What a ratio really means, how to simplify it, and the cross-multiplication trick for proportions.

By the PadhoDost Team · 📖 5 min read · Updated 4 August 2026

Part of SSC CGL & Banking prep

🧠 A recipe

A ratio is a recipe for mixing. '2 : 3' means for every 2 parts of one thing, take 3 of another. Double the recipe and it's still 2 : 3 — the relationship stays the same, only the amounts grow.

Simplifying a ratio

3 parts 2 parts 12 8 3 : 2 of 20 → 12 : 8
A ratio splits a whole into equal parts — 3 : 2 means 5 parts, so 20 splits as 12 and 8.

Divide both sides by their HCF. 12 : 18 → divide by 6 → 2 : 3. A ratio in its lowest terms is easiest to work with.

Proportion

A proportion says two ratios are equal: a : b = c : d. When that's true, the cross-products are equal.

If a : b = c : d then a × d = b × c

📝 Find x if 3 : 6 = 5 : x

Cross-multiply: 3 × x = 6 × 5

3x = 30

x = 10

💡 To split a quantity in a ratio, add the parts to get the total, then take each share as a fraction. Split ₹600 in 2 : 3 → 5 parts → A = 2/5 × 600 = ₹240.

⚡ Quick check

Divide ₹600 between A and B in the ratio 2 : 3. A's share is:

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