Ratio and the unitary method — Maths Olympiad practice
The unitary method means “go through one”: find the cost of one pen, the size of one part of a ratio, or the work of one worker — then scale up. Watch out for inverse questions: more workers take fewer days.
✓ You passed this topic’s test.
How to solve it
Go through one — “find the value of one thing (or one part), then multiply”
Unitary: cost of one = total ÷ number; then multiply by how many you need.
Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part.
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.
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
Fewer workers take longer: total work = 6 × 10 = 60 worker-days.
60 ÷ 4 = 15.
Check: 4 workers × 15 days = 60 worker-days, the same as 6 × 10 ✓
✏️ Practice
Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.
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🏁 Topic 13 test
20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.
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🖨️ Ratio and Unitary Method Worksheet for Olympiad
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