Ratios and proportions in EPSO numerical reasoning
How many times bigger is one figure than another, or how does a quantity scale. The division is easy; the work is in the order (A to B, not B to A) and in building each side of the ratio from the right cells.
4,684 answers, last 60 days · The test gives you 2 minutes per question (10 questions in 20 minutes).
How to recognise it
- What is the ratio of A to B?
- How many times larger is A than B and C combined?
- If 3 kg cost €12, how much do 7.5 kg cost?
The method
- Write the ratio in the order of the question: "A to B" means A ÷ B.
- Build each side from the cells it needs: if the question groups two countries, add them first.
- For a proportion, cross-multiply: unknown = known × (target ÷ reference).
Worked example
An example in EPSO format, written for this page.
| Country | 2021 | 2023 |
|---|---|---|
| Germany | 63.8 | 69.5 |
| Spain | 28.2 | 30.6 |
| France | 19.1 | 22.2 |
| Italy | 11.3 | 12.3 |
Unit: GW
In 2023, what is the ratio of Germany's wind capacity to the combined capacity of France and Italy?
Choose an answer to see the solution.
The traps
The inverted ratio
"A to B" is A ÷ B. The inverse is almost always an option, and it is easy to spot: it is below 1 when A is the bigger figure.
Half of a combined side
When the question groups items ("France and Italy combined"), forgetting one of them gives a ratio that is an option too.
The wrong year
Same rows, neighbouring column: in the example 2021 gives 2.10, very close to 2.01.
When the table cannot answer
A share of "the EU total" cannot be computed from a table that lists four countries. "Impossible to tell" is then the right answer, and EPSO uses it.
With the EPSO calculator
Add the combined side first and write it down (34.5), then divide. Typing 69.5 ÷ 22.2 + 12.3 without brackets divides by France only and adds Italy afterwards.
Practise this calculation
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Frequently asked questions
What does "the ratio of A to B" mean in EPSO tests?
A divided by B. The inverse (B ÷ A) is usually among the options.
How do I solve a proportion quickly?
Cross-multiply: if 3 kg cost €12, 7.5 kg cost 12 × 7.5 ÷ 3 = €30.