Eight questions. Eight reusable methods.
Practise percentages, weighted rates, targets, productivity, currency conversion and tiered commission using the tables below. Try each question before opening its explanation.
These are original ReasoningCampus exercises with fictional data, designed to practise numerical reasoning skills. They are not official SHL questions or a reproduction of an assigned assessment.
What this practice develops
Numerical reasoning asks you to interpret data and select the calculation that answers a particular question. An accurate calculation still gives the wrong answer if you use the wrong base, unit or comparison.
For a broader introduction, use the numerical reasoning guide. This page is a separate worked set, so you can apply the method to fresh data.
Choose a skill to practise
Questions 1–2 focus on percentage bases, 3–4 on combining and comparing data, 5–6 on reversing and scaling calculations, and 7–8 on applying multi-step rules.
Before you calculate
- Write down exactly what the question asks for, including its unit.
- Locate the relevant values and note which amounts are bases or thresholds.
- Estimate a plausible result, then calculate.
- Check the explanation and identify why each alternative is wrong.
Begin untimed. If you repeat the set, separate remembered answers from methods you can apply to an unseen question.
8 original numerical practice questions
Successive percentage changes
A shop recorded the sales below. Next month’s forecast is 10% above February. By what percentage would that forecast exceed January’s sales?
| Month | Sales |
|---|---|
| January | 24 |
| February | 30 |
Show answer and explanation
Correct answer: C. 37.5%
First find the forecast: £30,000 × 1.10 = £33,000. Compare it with January: (£33,000 − £24,000) ÷ £24,000 = 37.5%.
Why the other answers fail: 25% is January to February only. 35% adds 25% and 10% even though their bases differ. 10% compares the forecast with February, not January.
Change one condition: with a 20% rise from February, the forecast is £36,000 and the increase from January is 50%.
Profit margin, not markup
What is the operating profit margin as a percentage of revenue?
| Measure | Amount |
|---|---|
| Revenue | 80 |
| Operating costs | 62 |
Show answer and explanation
Correct answer: B. 22.5%
Profit = 80 − 62 = 18. Margin = profit ÷ revenue = 18 ÷ 80 = 22.5%.
A treats the profit amount as a percentage. C divides by cost and gives markup instead of margin. D is the cost share, 62 ÷ 80.
Reusable check: write the requested denominator before calculating. If costs rose to £68,000 with revenue unchanged, margin would fall to 12 ÷ 80 = 15%.
Weighted completion rates
What percentage of all participants completed the programme?
| Group | Participants | Completed |
|---|---|---|
| A | 40 | 75% |
| B | 60 | 50% |
Show answer and explanation
Correct answer: B. 60%
Completed in A: 40 × 0.75 = 30. Completed in B: 60 × 0.50 = 30. Combine counts before calculating the rate: (30 + 30) ÷ (40 + 60) = 60%.
A is the unweighted average of the two rates. C and D use only one group. The larger group has the lower rate, so the combined rate should be below 62.5%.
Change one condition: if both groups contained 40 people, the combined rate would be 62.5%. Equal weights make the simple average valid.
Largest proportional target excess
Which quarter exceeded its target by the largest percentage of that target?
| Quarter | Target | Actual |
|---|---|---|
| Q1 | 120 | 132 |
| Q2 | 180 | 198 |
| Q3 | 100 | 115 |
| Q4 | 160 | 176 |
Show answer and explanation
Correct answer: C. Q3
Use (actual − target) ÷ target. Q1: 12 ÷ 120 = 10%. Q2: 18 ÷ 180 = 10%. Q3: 15 ÷ 100 = 15%. Q4: 16 ÷ 160 = 10%.
Q2 has the largest absolute excess, £18,000, but Q3 has the largest proportional excess. A and D also represent only 10% above target.
Reusable check: “by how much” and “by what percentage” may produce different rankings.
Reverse a discount before adding a fee
A customer paid £306 for an item after a 15% discount. Delivery was not included. What would the original undiscounted item plus delivery cost?
| Item | Value |
|---|---|
| Discounted item price | £306 |
| Discount on original item price | 15% |
| Delivery fee | £18 |
Show answer and explanation
Correct answer: C. £378
£306 is 85% of the original price. Original = £306 ÷ 0.85 = £360. Add the unchanged delivery fee: £360 + £18 = £378.
A adds delivery to the discounted price. B increases £306 by 15%, which does not reverse a 15% discount, and omits delivery. D finds the original item price but stops too early.
Check backwards: £360 × 0.85 = £306. The fee is outside the discount calculation.
Output per person-hour
Assume all staff work at the same constant rate with no setup loss. How many units can 10 staff produce in 5 hours?
| Staff | Hours each | Units produced |
|---|---|---|
| 8 | 6 | 576 |
Show answer and explanation
Correct answer: C. 600
The observation contains 8 × 6 = 48 person-hours. Rate = 576 ÷ 48 = 12 units per person-hour. New capacity = 10 × 5 = 50 person-hours. Output = 50 × 12 = 600 units.
A changes only hours: 576 × 5 ÷ 6. D changes only headcount: 576 × 10 ÷ 8. B assumes the two changes cancel exactly; 48 and 50 person-hours are not equal.
Boundary: the constant-rate assumption is stated in this exercise. Do not assume it if a real question includes setup time or differing productivity.
Currency conversion with a fee
A business pays a €2,400 invoice using the stated exchange rate. A fee of 2% is then added to the converted sterling amount. What is the total sterling charge?
| Measure | Value |
|---|---|
| Invoice | €2,400 |
| Conversion rate | £0.85 for €1 |
| Fee | 2% of converted sterling amount |
Show answer and explanation
Correct answer: B. £2,080.80
Convert in the stated direction: €2,400 × £0.85 per euro = £2,040. Fee = £2,040 × 0.02 = £40.80. Total = £2,080.80.
A omits the fee. C adds 2% to the euro amount but treats it as pounds. D divides by 0.85 before adding 2%, reversing the quoted rate.
Reusable check: write the units alongside the rate. “Pounds per euro” cancels euros when you multiply.
Tiered commission
Sales total £38,000. Each commission rate applies only to the sales within its band. What is the total commission?
| Sales band | Rate on that band |
|---|---|
| First £20,000 | 2% |
| Next £10,000 | 4% |
| Sales above £30,000 | 6% |
Show answer and explanation
Correct answer: B. £1,280
First band: £20,000 × 2% = £400. Second band: £10,000 × 4% = £400. Remaining sales: (£38,000 − £30,000) × 6% = £480. Total = £1,280.
A applies 2% to everything. C applies 4% to everything. D applies the highest rate to all sales. Each ignores the marginal-band instruction.
Boundary check: at exactly £30,000, commission would be £800. Only sales above that threshold receive 6%.
Review the cause, not just the score
| Question | What went wrong | Next action |
|---|---|---|
| Example: Q3 | Averaged rates without weights | Reconstruct the number completing in each group |
| Example: Q5 | Added 15% instead of reversing a discount | Identify the remaining percentage before dividing |
| Example: Q8 | Applied the top rate to every sale | Split the total at each threshold |
Build a focused practice routine
Pick the two methods that caused most difficulty. Explain each without looking at the answer, then use a new example from the linked lessons. Add timing only after the setup is reliable.
Reverse percentages · Weighted averages · Chart units and ratios
Check your actual assessment instructions
Question format, time limits, calculator rules and navigation depend on the assigned assessment. Follow your invitation and official familiarisation activity. This lesson does not set an official time limit or convert your result into a percentile.
Use the explanations to transfer the method
The changed-condition checks show how an answer responds when one value changes. That is more informative than memorising a letter: you should be able to explain both the operation and its denominator.
Sources and next steps
SHL’s official practice resources provide provider familiarisation. All questions, fictional datasets and worked calculations on this page were created for ReasoningCampus.
Return to the numerical reasoning guide · Try a mixed reasoning question set · Explore SHL preparation
