Arithmetic
What the Arithmetic section tests
The arithmetic paper is speed-based: percentages, ratio and proportion, averages, profit and loss, simple interest, time–work, and time–distance. Most errors come from choosing the wrong base, not from hard calculation.
Core rules
- Percentage change = (change ÷ original) × 100; the original is the base.
- Successive percentage changes do not add: a 20% rise then a 10% fall gives 1.20 × 0.90 = 1.08, a net 8% rise.
- Profit% and loss% are calculated on cost price unless the question states otherwise.
- Simple interest = principal × rate × time ÷ 100.
- Average = total ÷ number of items; to combine averages, use totals, not the averages themselves.
- Work rates add: if A finishes in 6 days and B in 3, their combined rate is 1/6 + 1/3 = 1/2, so they finish in 2 days.
Worked example
A price is discounted by 20%, then by 10%. What is the single equivalent discount? Reasoning: after the first discount the customer pays 80% of the marked price. After the second, the customer pays 90% of that: 0.80 × 0.90 = 0.72. The customer pays 72%, so the equivalent discount is 28%, not 30%.
Traps that cost marks
- Adding 20% and 10% to get 30%.
- Taking profit percentage on selling price instead of cost price.
- Averaging two averages without weighting by group size.
- Mixing units, e.g. minutes and hours in a time–work problem.
- Applying a percentage increase and then the same percentage decrease and assuming the original value returns.