Word problems & business scenarios in numerical tests
By Marin Devereux·6 min read·
Word problems are numerical questions disguised as business stories. The maths rarely goes beyond GCSE level — percentages, ratios, simple algebra. The challenge is extracting the numbers from the narrative before time runs out.
The five recurring business scenarios
- Profit & margin — revenue minus cost, margin as a percentage of revenue.
- Discount & markup — original price, discount %, sale price. Watch for successive discounts.
- Rates & productivity — units per hour, machines per shift. Classic work-rate problems.
- Capacity & utilisation — a factory can produce X units; it ran at Y%. How many were made?
- Growth & compound change — year-on-year growth applied over multiple periods.
Profit margin
A product costs $45 to produce and sells for $72. If the company sells 1,200 units, what is the total profit and profit margin?
Profit per unit = $72 − $45 = $27. Total profit = 27 × 1,200 = $32,400.
Margin = 27 / 72 = 37.5%. Remember: margin is profit over revenue, not profit over cost.
Successive discounts
A jacket is marked at $200. It receives a 20% discount, then a further 10% off the reduced price. What is the final price?
After 20% off: $200 × 0.80 = $160. After 10% off: $160 × 0.90 = $144.
Trap: candidates add 20% + 10% = 30% and answer $140. Successive discounts compound — they do not add.
Work rate
Machine A produces 120 units/hour. Machine B produces 80 units/hour. Working together, how long to produce 1,000 units?
Combined rate = 200 units/hour. Time = 1,000 / 200 = 5 hours.
The translation habit
Read the problem once for the story. Read it a second time to underline every number and its unit. Then — and only then — set up the calculation. This two-pass approach prevents the most common error: using the wrong number in the right formula.
Speed tips for word problems
- Round first, refine later. If exact answers are not in the options, estimation gets you there faster.
- Work backwards from the options. If you are stuck, plug each option into the scenario and see which one fits.
- Watch for distractor data. Word problems often include numbers you do not need. Only extract what the question asks for.
Practise business scenarios on forge
Numerical packs with real business mini-cases — revenue, cost, growth, and capacity — across SHL and Forge formats.
Start practising