Percentages & ratios

A jacket originally priced at £80 is reduced by 25% in a sale. What is the sale price?

• A£60✓
• B£75
• C£65
• D£55

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?

• A50%
• B20%
• C30%
• D25%✓

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?

• A175g
• B70g
• C140g✓
• D100g

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£45.00
• C£44.00
• 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£18,000
• D£15,000✓

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£30,000✓
• B£30,600
• C£29,568
• 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£80✓
• B£75
• C£90
• D£84

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.

A solution is 30% acid by volume. How much pure acid is in 2.5 litres of the solution?

• A0.75 litres✓
• B0.70 litres
• C0.65 litres
• D0.55 litres

Answer: 30% of 2.5 litres = 0.30 × 2.5 = 0.75 litres.

Two numbers are in the ratio 7:9. If their sum is 320, what is the larger number?

• A140
• B160
• C180✓
• D200

Answer: Total parts = 16; each part = 320 ÷ 16 = 20; larger = 9 × 20 = 180.

A stock fell by 20% one week and then rose by 30% the following week. By what overall percentage did it change from its starting value?

• AUp 6%
• BDown 6%
• CUp 10%
• DUp 4%✓

Answer: Multiplier = 0.80 × 1.30 = 1.04, an overall increase of 4%.

A factory's defect rate dropped from 8% to 5%. By what percentage did the defect rate fall, relative to the original rate?

• A3%
• B37.5%✓
• C30%
• D60%

Answer: The fall is 3 percentage points; relative to 8% that is 3 ÷ 8 = 0.375 = 37.5%.

A budget of £24,000 is divided between three departments in the ratio 2:3:7. How much does the largest department receive?

• A£9,000
• B£16,000
• C£12,000
• D£14,000✓

Answer: Total parts = 12; each part = £24,000 ÷ 12 = £2,000; largest = 7 × £2,000 = £14,000.