Maths Olympiad · topic 17 of 33 · free

Averages — Maths Olympiad practice

The key to average puzzles is the total: average × how many numbers = total. When a number is taken away or added, compare the totals before and after — the difference is the number.

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How to solve it

Think in totals — “turn every average into a total, work with the totals, then divide”

Average = total ÷ how many; so total = average × how many.
A number taken away = old total − new total.
Evenly spaced numbers (like 10 to 20): average = (first + last) ÷ 2.

Use it for: Marks, cricket scores, ages and every average question in Class 6–10.

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

Worked example: The average of 5 numbers is 30. When one number is taken away, the average of the rest is 28. Which number was taken away? → 38

Total of all 5 = 5 × 30 = 150.
Total of the other 4 = 4 × 28 = 112.
The number taken away = 150 − 112 = 38.

Check: 112 + 38 = 150 and 150 ÷ 5 = 30 ✓

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✓ Written and checked by the TalentJR team · Updated 13 Oct 2026 · How we make our lessons

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