Percentage Calculations and Percentage Change
EPSO numerical reasoning leans on percentages more than on any other single skill. The questions rarely ask for a bare percentage: they ask you to move between a value, a base and a change, often twice, and to decide which of the three is the base in a particular sentence. The arithmetic is easy; the marks are lost on base selection and on treating successive changes as additive.
The four core relationships
- Percentage of a quantity: p% of X = X × p/100.
- Percentage change: ((new − old) / old) × 100. The base is always the starting value, never the new one.
- Forward multipliers: +p% means multiply by (1 + p/100); −p% means multiply by (1 − p/100).
- Reverse multipliers: if a price after a 15% rise is €92, the original is 92 / 1.15 = €80. Divide by the multiplier; never subtract the percentage from the final figure.
Successive changes
Changes compound multiplicatively. A 20% rise followed by a 10% fall gives 1.20 × 0.90 = 1.08, i.e. +8%, not +10%. Order does not affect the final value, but it does affect which year saw the larger movement.
Percentage points versus per cent
A share moving from 20% to 25% has risen 5 percentage points but 25% relatively (5/20). Both figures are routinely offered as answer options.
Worked example
A programme's budget is €240m. It rises 20% in year 1, then falls 10% in year 2. What is the overall change and the final figure?
Year 1: 240 × 1.20 = 288. Year 2: 288 × 0.90 = 259.2. The overall multiplier is 1.20 × 0.90 = 1.08, so +8% and €259.2m. The tempting answer, 20 − 10 = 10%, is wrong because the fall is applied to a larger base.
Traps
- Using the post-change value as the base for a fall (288 − 28.8 taken as the original).
- Adding successive percentages instead of multiplying their multipliers.
- Reading "A is 20% more than B" as "B is 20% less than A" - B is in fact 16.7% less.
- Rounding the multiplier mid-calculation and losing the digit that separates two options.