Ratio and the unitary method — Maths Olympiad practice

How to solve it

Go through one — “find the value of one thing (or one part), then multiply”

1. Unitary: cost of one = total ÷ number; then multiply by how many you need.
2. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part.
3. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

Use it for: Prices, recipes, sharing in a ratio, and time-and-work questions in Class 5–8.

🧮 Check your own sums with the free Ratio calculator — it shows the working.

Worked example: 6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? 15 days

✏️ Practice

Work it out on paper, then tap the answer you think is right. Stuck? Press “Show me how” to see every step.

🏁 Topic 13 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

🏅 Sign in with Google to earn the 🛒 Money Puzzle Pro badge when you pass — and a certificate when you finish all 7 topics of Part 2 · Class 5–7. You can still take the test without signing in.

🖨️ Ratio and Unitary Method Worksheet for Olympiad

• Worksheet set 1 (PDF)
• Worksheet set 2 (PDF)
• Worksheet set 3 (PDF)