Numeracy and fares: questions and answers
45 practice questions for UK taxi and private hire knowledge tests, with answers and explanations at the end.
Free from taxiknowledgetest.co.uk. Not an official council document: check your council's current guidance.
Questions
Working out a fare
A tariff is £3.20 for the first mile, then £2.00 for each mile after that. What is the fare for a 5-mile journey?
The meter starts at £2.60 (the flag fall) and adds £1.80 for every mile. What is the fare for 4 miles?
A tariff is £3.00 for the first mile, then 25p for each fifth of a mile or part of a fifth. What is the fare for 2.5 miles?
The flag fall is £3.50 and covers the first half mile. After that it is 20p for each tenth of a mile. What is the fare for 3 miles?
The flag fall is £2.50 and covers the first half mile. After that it is 20p for each tenth of a mile. What is the fare for 3.2 miles?
The meter shows £8.40 for the distance. You also waited 7 minutes, and waiting time is 30p a minute. What is the total fare?
Waiting time is charged at 20p for every 30 seconds. A passenger keeps you waiting for 4 minutes. What is the waiting charge?
A journey costs £12.00 on the day tariff. The night tariff is 1.5 times the day tariff. What does the same journey cost at night?
A journey costs £10.40 on the normal tariff. On a bank holiday the tariff is 50% higher. What does the journey cost on a bank holiday?
The meter shows £14.60. The table of fares adds £1.00 for each passenger after the first. There are 4 passengers. What is the total?
The tariff is a £3.00 flag fall plus £1.50 for each mile. The fare was £9.00. How many miles was the journey?
Giving change and splitting fares
The fare is £13.40. The passenger pays with a £20 note. How much change do you give?
The fare is £7.65. The passenger pays with a £10 note. How much change do you give?
The fare is £26.80. The passenger gives you a £20 note and a £10 note. How much change do you give?
The fare is £18.75. The passenger pays with a £50 note. How much change do you give?
The fare is £11.30. The passenger gives you £15 and says 'keep £1 as a tip'. How much change do you give?
The fare is £5.90. The passenger gives you £10.40 so that the change is easier. How much change do you give?
You owe a passenger £4.80 in change. You have £2, £1, 50p, 20p and 10p coins. What is the smallest number of coins you can give?
Three passengers share a fare of £24.60 equally. How much does each one pay?
Four friends share a fare of £31.00 equally. How much does each one pay?
The fare is £13.20. One passenger gives you £10 and the other gives you £5. How much change do you give in total?
The fare is £14.50. The passenger paid with a £20 note and you gave back £5.00. How much more change do you owe?
Journey times and the 24-hour clock
You drive 12 miles at an average speed of 24 mph. How long does the journey take?
You drive 45 miles at an average speed of 30 mph. How long does the journey take?
You drive 8 miles at an average speed of 20 mph. How long does the journey take?
You drive for 36 minutes at an average speed of 30 mph. How far do you travel?
You leave at 14:35. The journey takes 50 minutes. What time do you arrive?
You pick up a passenger at 22:30. The journey takes 1 hour 45 minutes. What time do you arrive?
A passenger must be at the station by 08:10. The journey takes 25 minutes and you want 5 minutes spare. What is the latest time to pick them up?
A passenger books a car for 7.45 pm. How is this written in the 24-hour clock?
A booking is for 00:20. When is that?
What is 15:05 in the 12-hour clock?
A night tariff runs from 23:00 to 06:00. Which of these start times is in the night tariff?
Earnings, fuel and percentages
Your operator takes 15% commission. Your fares this week total £600. How much commission do you pay?
You take £840 in fares in a week. You pay £120 radio rent to the operator and £95 for fuel. How much is left?
Your car uses 1 litre of fuel every 8 miles. You drive 240 miles. Fuel costs £1.45 a litre. What does the fuel cost?
Your electric car uses 0.25 kWh for each mile. You drive 120 miles. Electricity costs 28p per kWh. What does the electricity cost?
The council puts up fares by 4%. A journey used to cost £12.50. What does it cost now?
A card payment company charges 1.75% of each payment. A passenger pays a £40 fare by card. What is the charge?
An account customer gets 10% off. The fare is £22.00. What do they pay?
You earn £168 in an 8-hour shift. How much is that for each hour?
A fixed price job pays £45 for 30 miles. How much is that per mile?
The mileage reading was 45,280 at the start of your shift and 45,463 at the end. How many miles did you drive?
An operator rounds fares up to the next 10p. The worked-out fare is £14.63. What does the passenger pay?
Your vehicle is licensed to carry 4 passengers. A group of 7 people want to travel together. How many vehicles do they need?
Answers
- C. £11.20. The first mile costs £3.20. That leaves 4 miles at £2.00 = £8.00. £3.20 + £8.00 = £11.20.
- B. £9.80. 4 miles × £1.80 = £7.20. Add the flag fall: £7.20 + £2.60 = £9.80.
- B. £5.00. After the first mile there are 1.5 miles left. That is 7.5 fifths, and a part counts as a whole, so 8 × 25p = £2.00. £3.00 + £2.00 = £5.00.
- B. £8.50. After the first half mile there are 2.5 miles left = 25 tenths. 25 × 20p = £5.00. £3.50 + £5.00 = £8.50.
- D. £7.90. 3.2 – 0.5 = 2.7 miles = 27 tenths. 27 × 20p = £5.40. £2.50 + £5.40 = £7.90.
- D. £10.50. 7 minutes × 30p = £2.10. £8.40 + £2.10 = £10.50.
- A. £1.60. 4 minutes = 8 lots of 30 seconds. 8 × 20p = £1.60.
- B. £18.00. 1.5 times £12.00 = £12.00 + £6.00 = £18.00.
- C. £15.60. 50% of £10.40 is £5.20. £10.40 + £5.20 = £15.60.
- A. £17.60. Only passengers after the first are charged: 3 × £1.00 = £3.00. £14.60 + £3.00 = £17.60.
- A. 4 miles. Take off the flag fall: £9.00 – £3.00 = £6.00. £6.00 ÷ £1.50 = 4 miles.
- B. £6.60. £20.00 – £13.40 = £6.60. Check: £13.40 + £6.60 = £20.00.
- A. £2.35. £10.00 – £7.65 = £2.35. Check: £7.65 + £2.35 = £10.00.
- A. £3.20. £20 + £10 = £30.00. £30.00 – £26.80 = £3.20.
- D. £31.25. £50.00 – £18.75 = £31.25. Check: £18.75 + £31.25 = £50.00.
- A. £2.70. £15.00 – £11.30 = £3.70. Take off the £1 tip: £3.70 – £1.00 = £2.70.
- C. £4.50. £10.40 – £5.90 = £4.50. Check: £5.90 + £4.50 = £10.40.
- D. 5 coins. £2 + £2 + 50p + 20p + 10p = £4.80. That is 5 coins.
- D. £8.20. £24.60 ÷ 3 = £8.20. Check: 3 × £8.20 = £24.60.
- C. £7.75. £31.00 ÷ 4 = £7.75. Check: 4 × £7.75 = £31.00.
- A. £1.80. £10 + £5 = £15.00. £15.00 – £13.20 = £1.80.
- D. 50p. The correct change is £20.00 – £14.50 = £5.50. You gave £5.00, so you still owe 50p.
- B. 30 minutes. Time = distance ÷ speed. 12 ÷ 24 = 0.5 hours, which is 30 minutes.
- D. 1 hour 30 minutes. 45 ÷ 30 = 1.5 hours. Half an hour is 30 minutes, so the journey takes 1 hour 30 minutes, not 1 hour 50.
- A. 24 minutes. 8 ÷ 20 = 0.4 hours. 0.4 × 60 = 24 minutes.
- C. 18 miles. 36 minutes is 0.6 of an hour. 0.6 × 30 = 18 miles.
- D. 15:25. 14:35 + 25 minutes = 15:00. Add the other 25 minutes: 15:25.
- C. 00:15. 22:30 + 1 hour = 23:30. 23:30 + 45 minutes = 00:15, which is a quarter past midnight. The clock goes back to 00 after 23:59.
- C. 07:40. 25 + 5 = 30 minutes. 08:10 – 30 minutes = 07:40.
- B. 19:45. For pm times, add 12 to the hour: 7 + 12 = 19, so 7.45 pm is 19:45.
- B. 20 minutes past midnight. 00:20 in the 24-hour clock is 12.20 am: 20 minutes after midnight.
- D. 3.05 pm. Take 12 away from hours after 12: 15 – 12 = 3, so 15:05 is 3.05 pm.
- C. 05:30. 05:30 is between 23:00 and 06:00, so it is in the night tariff. 06:15, 22:45 and 18:00 are all outside it.
- B. £90. 10% of £600 is £60 and 5% is £30. 15% = £60 + £30 = £90. (£510 is what you keep, not the commission.)
- A. £625. £120 + £95 = £215. £840 – £215 = £625.
- C. £43.50. 240 ÷ 8 = 30 litres. 30 × £1.45 = £43.50.
- B. £8.40. 120 × 0.25 = 30 kWh. 30 × 28p = £8.40. (£33.60 is 120 × 28p, which forgets the 0.25.)
- D. £13.00. 1% of £12.50 is 12.5p, so 4% is 50p. £12.50 + £0.50 = £13.00.
- A. 70p. 1% of £40 is 40p. 1.75 × 40p = 70p.
- A. £19.80. 10% of £22.00 is £2.20. £22.00 – £2.20 = £19.80.
- C. £21. £168 ÷ 8 = £21 an hour.
- B. £1.50. £45 ÷ 30 = £1.50 a mile.
- D. 183 miles. 45,463 – 45,280 = 183 miles.
- C. £14.70. Rounding up to the next 10p turns £14.63 into £14.70. £14.60 would be rounding down.
- A. 2 vehicles. 7 ÷ 4 = 1.75, and you cannot send part of a vehicle, so round up to 2. Never carry more passengers than your licence allows.
Sources
- Taxi and private hire driver tests and certificates, Bristol City Council, Undated web page. Lists 'how to calculate change and general road safety' as a test subject.. Checked 29 October 2026. https://www.bristol.gov.uk/business/licences-and-permits/taxis-and-private-hire-licensing/taxi-driver-tests-and-certificates
- Application for a Combined Hackney Carriage Private Hire Driver Licence, Nottingham City Council, Undated web page. The Topography Test includes a Numeracy section.. Checked 29 October 2026. https://nottinghamcity.gov.uk/information-for-business/business-information-and-support/business-and-trading-licences-and-permits/taxi-licensing/apply-for-a-taxi-licence/combined-hackney-carriage-and-private-hire-licence
- Stage 3: skills and knowledge test, stage 4: licence review, stage 5: licence issued, Manchester City Council, Undated web page. The council site blocked our reader, so we confirmed the skills assessment description (literacy, comprehension, numeracy and the Highway Code) from the search engine's copy of the page.. Checked 29 October 2026. https://www.manchester.gov.uk/taxis-and-private-hire/taxi-and-private-hire-drivers-information/become-a-licensed-hackney-carriage-or-private-hire-driver-in-manchester/stage-3-skills-and-knowledge-test-stage-4-licence-review-stage-5-licence-issued
- Local Government (Miscellaneous Provisions) Act 1976, section 65 (fixing of fares for hackney carriages), legislation.gov.uk, Revised text, up to date to 29 October 2026.. Checked 29 October 2026. https://www.legislation.gov.uk/ukpga/1976/57/section/65