25 numerical reasoning practice questions with worked answers
By Marin Devereux·12 min read·
Below are 25 free numerical reasoning questions with step-by-step worked answers. They are grouped by question family so you can drill the patterns that repeat on real tests: percentages, ratios, weighted averages, rates, and multi-step chart interpretation.
How to use these questions
Do not just read the answers. Attempt each question first, then check the method. If you got it wrong, write down which step failed — that is your error category.
Percentages (Questions 1–5)
Q1
A product costs £80. It is discounted by 15%. What is the sale price?
15% of £80 = 10% (£8) + 5% (£4) = £12. Sale price = £80 − £12 = £68.
Q2
Revenue grew from £2.4m to £3.0m. What is the percentage increase?
Increase = £0.6m. % = 0.6 / 2.4 = 0.25 = 25%.
Q3
After a 20% discount, an item costs £56. What was the original price?
£56 = 80% of original. Original = 56 / 0.80 = £70.
Q4
A company’s costs increased by 12% to £336,000. What were the original costs?
£336,000 = 112% of original. Original = 336,000 / 1.12 = £300,000.
Q5
Sales were £500k in Q1 and £575k in Q2. In Q3 they fell 8% from Q2. What were Q3 sales?
8% of £575k = £46k. Q3 = £575k − £46k = £529k.
Ratios (Questions 6–10)
Q6
A recipe uses flour and sugar in a 3:1 ratio. If you use 450g of flour, how much sugar?
1 part = 450 / 3 = 150. Sugar = 150g.
Q7
A team of 24 is split into developers and designers in a 5:1 ratio. How many developers?
Total parts = 6. Developers = (5/6) × 24 = 20.
Q8
Profit is shared between A, B, C in ratio 2:3:5. Total profit is £40,000. What does B get?
Total parts = 10. B = (3/10) × £40,000 = £12,000.
Q9
A drink is mixed water:concentrate 4:1. You have 2 litres of concentrate. How much water?
If concentrate = 1 part = 2L, then water = 4 parts = 8 litres.
Q10
Men to women in a department is 3:2. There are 45 people total. How many women?
Total parts = 5. Women = (2/5) × 45 = 18.
Weighted averages (Questions 11–15)
Q11
Product A costs £10 (sold 200 units). Product B costs £15 (sold 300 units). What is the weighted average price?
3 workers complete 18 tasks in 6 hours. What is the rate per worker per hour?
18 / (3×6) = 18/18 = 1 task per worker per hour.
Q17
A machine produces 240 widgets in 8 hours. How many in 5 hours?
Rate = 240/8 = 30/hour. In 5 hours = 150 widgets.
Q18
Electricity costs 14p per kWh. A device uses 2.5 kWh per day. Monthly cost (30 days)?
2.5 × 14 × 30 = 1050p = £10.50.
Q19
A car travels 180 miles on 6 gallons. How far on 10 gallons?
Rate = 30 miles/gallon. 10 × 30 = 300 miles.
Q20
A data entry team of 4 processes 1200 records in 3 days. How long for 2000 records with 5 people?
Rate = 1200 / (4×3) = 100 records per person-day. 2000 / (5×100) = 4 days.
Multi-step chart questions (Questions 21–25)
Quarterly sales by region (£k)
Use this chart for questions 21–25.
Q21
What was the total sales across both regions in Q1?
120 + 95 = £215k.
Q22
By what percentage did North sales grow from Q1 to Q2?
(145 − 120) / 120 = 25/120 = 20.8%.
Q23
What proportion of total Q2 sales came from the South region?
Total Q2 = 145 + 110 = 255. South share = 110/255 = 43.1%.
Q24
If North Q3 sales grow at the same rate as Q1→Q2, what will North Q3 be?
Growth rate = 20.8%. Q3 = 145 × 1.208 = £175.2k.
Q25
South’s Q2 target was £120k. By how much did they miss the target?
Shortfall = £120k − £110k = £10k (missed by 8.3%).
What to do next
Count your errors by family. If most wrong answers are in one section, that is your priority for the next practice session. Do not practise all 25 again — drill the family that cost you the most marks.
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