Percentages & ratios
17 free practice questions with explanations
PassNova has 17 free Numerical Reasoning Test practice questions on Percentages & ratios, each with a clear explanation. Practise them in the browser with instant feedback — 100% free, no sign-up, on any device. Updated for 2026.
Percentages & ratios: example questions & answers
12 worked examples with answers and explanations below. Practise all 17 Percentages & ratios questions free in the browser, with instant feedback on every answer.
A jacket originally priced at £80 is reduced by 25% in a sale. What is the sale price?
- A£55
- B£60✓
- C£65
- D£75
Answer: 25% of £80 is £20, so the sale price is £80 - £20 = £60.
In a class of 30 students, the ratio of boys to girls is 2:3. How many girls are there?
- A12
- B15
- C18✓
- D20
Answer: The ratio 2:3 has 5 parts; 30 ÷ 5 = 6 per part, so girls = 3 × 6 = 18.
A company's revenue rose from £200,000 to £250,000 in one year. What was the percentage increase?
- A20%
- B25%✓
- C30%
- D50%
Answer: The increase is £50,000; £50,000 ÷ £200,000 = 0.25 = 25%.
A recipe uses flour and sugar in the ratio 5:2. If 350g of flour is used, how much sugar is needed?
- A70g
- B100g
- C140g✓
- D175g
Answer: Each part of flour = 350 ÷ 5 = 70g; sugar = 2 × 70 = 140g.
What is 15% of 240?
- A24
- B30
- C36✓
- D40
Answer: 15% of 240 = 0.15 × 240 = 36.
A shop increases a £45 item by 20%, then later reduces the new price by 20%. What is the final price?
- A£43.20✓
- B£44.00
- C£45.00
- D£46.80
Answer: £45 × 1.20 = £54, then £54 × 0.80 = £43.20; successive ±20% does not return to the start.
Three partners share profits in the ratio 3:4:5. If the total profit is £36,000, how much does the partner with the largest share receive?
- A£9,000
- B£12,000
- C£15,000✓
- D£18,000
Answer: Total parts = 12; each part = £36,000 ÷ 12 = £3,000; largest share = 5 × £3,000 = £15,000.
A population of 8,000 grows by 5% in year one and a further 10% in year two. What is the population after two years?
- A8,400
- B9,000
- C9,240✓
- D9,600
Answer: 8,000 × 1.05 = 8,400, then 8,400 × 1.10 = 9,240.
After a 12% pay rise, an employee earns £33,600. What was the salary before the rise?
- A£29,568
- B£30,000✓
- C£30,600
- D£36,000
Answer: Original × 1.12 = £33,600, so original = £33,600 ÷ 1.12 = £30,000.
A mixture contains red, blue and green tokens in the ratio 4:5:6. If there are 90 tokens in total, how many are blue?
- A24
- B30✓
- C36
- D45
Answer: Total parts = 15; each part = 90 ÷ 15 = 6; blue = 5 × 6 = 30.
An item costs £60 after a 25% discount. What was its original price?
- A£75
- B£80✓
- C£84
- D£90
Answer: £60 represents 75% of the original; original = £60 ÷ 0.75 = £80.
In a survey, 35% of 1,200 respondents preferred brand A and 40% preferred brand B. How many preferred neither brand A nor brand B?
- A240
- B300✓
- C420
- D480
Answer: A and B together = 75%, so neither = 25% of 1,200 = 300.