Basic Mathematics and Business Applications
This domain tests whether you can turn business wording into arithmetic: percentage change and reverse percentages, ratio sharing, markup versus margin, compounded growth, currency conversion and break-even. ICAP questions usually hide one interpretation step before the calculation.
Core rules
- Percentage change = (new − old)/old × 100. To reverse a percentage change, divide by the multiplier: a price of 680 after a 15% discount means list = 680/0.85.
- Markup is a percentage of cost; margin is a percentage of selling price. If cost is 680 and markup is 25%, selling price = 850 and margin = 170/850 = 20%.
- Share a total in a ratio by dividing by the sum of the ratio parts.
- Compound growth: final = initial(1 + g)^n. The average compound rate is (final/initial)^(1/n) − 1, not the arithmetic mean of yearly rates.
- Break-even units = fixed costs / contribution per unit.
Worked example
A retailer buys at a list price of 800 less a 15% trade discount. It marks up cost by 25%. Find the selling price and gross margin. Cost = 800 × 0.85 = 680. Markup = 0.25 × 680 = 170. Selling price = 850. Margin = 170/850 = 20%. The discount is deducted from list; the markup is added to cost, so the two percentages apply to different bases.
Traps
- Taking 15% of 680 instead of dividing by 0.85.
- Treating a 25% markup as a 25% margin.
- Adding successive percentage changes: +20% then −20% gives 96%, not 100%.
- Using simple average growth for compounding.