Reverse percentages in EPSO numerical reasoning
You know the value after a change, or a part and its share, and you need the starting value or the total. The reflex of applying the percentage again goes the wrong way: the method is to divide.
3,744 answers, last 60 days · The test gives you 2 minutes per question (10 questions in 20 minutes).
How to recognise it
- Pears were 16% of total fruit production: what was total fruit production?
- After a 20% rise the price is €60. What was it before?
- What was the 2021 value, if it grew by 9% to reach the 2022 figure?
The method
- Write the known value as the unknown times a factor: a 16% share is × 0.16, after a 20% rise × 1.20, after a 15% fall × 0.85.
- Divide the known value by that factor.
- For several successive changes, divide by each factor in turn.
Worked example
A question from our bank, in EPSO format.
| Country | Pear production 2019 (thousand t) | Share of fruit 2019 (%) | Pear production 2022 (thousand t) | Share of fruit 2022 (%) |
|---|---|---|---|---|
| Buldonia | 216 | 16 | 312 | 12 |
| Venalia | 420 | 20 | 340 | 22 |
| Telonia | 42 | 4 | 36 | 2 |
What was the average annual fruit production of Buldonia in 2019 and 2022 combined?
Choose an answer to see the solution.
The traps
Multiplying instead of dividing
Taking 20% off a price of €60 gives €48, but the price before a 20% rise was €60 ÷ 1.20 = €50. The percentage applies to the unknown starting value, not to the figure you can see.
Adding successive changes
A fall of 20% followed by a fall of 15% is not a fall of 35%: divide by 0.85, then by 0.80.
Stopping at the part
When the question asks for the total, the share is only the way to it. In the example, the average of pears (264 thousand t) is among the options.
With the EPSO calculator
Divide by the factor directly: 216 ÷ 0.16. For a 15% fall, divide by 0.85. Multiplying by 1.15 is a different (and wrong) calculation.
Practise this calculation
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Frequently asked questions
How do I find the original value after a percentage increase?
Divide the new value by (1 + rate). After a 20% rise to €60, the original was 60 ÷ 1.20 = €50, not €48.
How do I find a total from a share?
Divide the part by its share: if 216 thousand tonnes are 16% of the total, the total is 216 ÷ 0.16 = 1,350 thousand tonnes.