Percentage Calculations

Percentage questions are the most frequently tested topic in UCAT Quantitative Reasoning. They appear in nearly every data set — calculating percentage increases, finding what percentage one value is of another, working backwards from a percentage, and handling compound changes. This lesson covers every type of percentage calculation you will encounter, with efficient methods for each.

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Type 1: Finding X% of Y

The most basic percentage calculation.

Formula: X% of Y = (X ÷ 100) × Y

The Building-Block Method

Break any percentage into components you can calculate instantly:

Component	How to Find It
50%	Halve the number
10%	Divide by 10
5%	Half of 10%
1%	Divide by 100
25%	Divide by 4 (or halve 50%)

Example: Find 35% of 840

• 10% of 840 = 84
• 30% = 3 × 84 = 252
• 5% = 84 ÷ 2 = 42
• 35% = 252 + 42 = 294

Example: Find 17% of 6,000