Numeracy and fares: questions and answers
Based on Taxi and private hire driver tests and certificates (Bristol City Council, dates under Sources) and 3 other sources. Checked .
Many councils test basic maths as part of the knowledge test. Bristol's test includes how to calculate change. Nottingham's test has a numeracy section. Manchester's skills assessment checks numeracy as well as reading and the Highway Code. The questions are the sums a driver does at work: working out a fare from a tariff, adding waiting time and extras, giving change, splitting a fare, and working out journey times.
Fares and tariffs are different in every council area. For hackney carriages, the council sets the maximum fares in a table of fares, and the meter must follow it. Private hire fares are agreed in advance, or set by the operator when you book. The tariffs in these questions are made up for practice. Always use your own council's table of fares at work.
Every figure you need is in the question. Read the tariff carefully: check what the first charge (the flag fall) covers, and whether part of a mile is charged as a whole unit. The wrong answers are the usual mistakes, such as forgetting the flag fall or giving the wrong change.
45 questions in 4 sets. Answer one set at a time and you'll see the right answer straight away. Every question and answer is also listed below and in a free PDF.
Working out a fare
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Question 1 of 11
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?
All 45 questions and answers
Open a set to see each question, the right answer and why.
Working out a fare11 questions
1. 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?
Answer: C. £11.20. The first mile costs £3.20. That leaves 4 miles at £2.00 = £8.00. £3.20 + £8.00 = £11.20.
2. The meter starts at £2.60 (the flag fall) and adds £1.80 for every mile. What is the fare for 4 miles?
Answer: B. £9.80. 4 miles × £1.80 = £7.20. Add the flag fall: £7.20 + £2.60 = £9.80.
3. 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?
Answer: 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.
4. 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?
Answer: 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.
5. 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?
Answer: D. £7.90. 3.2 – 0.5 = 2.7 miles = 27 tenths. 27 × 20p = £5.40. £2.50 + £5.40 = £7.90.
6. 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?
Answer: D. £10.50. 7 minutes × 30p = £2.10. £8.40 + £2.10 = £10.50.
7. Waiting time is charged at 20p for every 30 seconds. A passenger keeps you waiting for 4 minutes. What is the waiting charge?
Answer: A. £1.60. 4 minutes = 8 lots of 30 seconds. 8 × 20p = £1.60.
8. 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?
Answer: B. £18.00. 1.5 times £12.00 = £12.00 + £6.00 = £18.00.
9. 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?
Answer: C. £15.60. 50% of £10.40 is £5.20. £10.40 + £5.20 = £15.60.
10. 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?
Answer: A. £17.60. Only passengers after the first are charged: 3 × £1.00 = £3.00. £14.60 + £3.00 = £17.60.
11. 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?
Answer: A. 4 miles. Take off the flag fall: £9.00 – £3.00 = £6.00. £6.00 ÷ £1.50 = 4 miles.
Giving change and splitting fares11 questions
12. The fare is £13.40. The passenger pays with a £20 note. How much change do you give?
Answer: B. £6.60. £20.00 – £13.40 = £6.60. Check: £13.40 + £6.60 = £20.00.
13. The fare is £7.65. The passenger pays with a £10 note. How much change do you give?
Answer: A. £2.35. £10.00 – £7.65 = £2.35. Check: £7.65 + £2.35 = £10.00.
14. The fare is £26.80. The passenger gives you a £20 note and a £10 note. How much change do you give?
Answer: A. £3.20. £20 + £10 = £30.00. £30.00 – £26.80 = £3.20.
15. The fare is £18.75. The passenger pays with a £50 note. How much change do you give?
Answer: D. £31.25. £50.00 – £18.75 = £31.25. Check: £18.75 + £31.25 = £50.00.
16. The fare is £11.30. The passenger gives you £15 and says 'keep £1 as a tip'. How much change do you give?
Answer: A. £2.70. £15.00 – £11.30 = £3.70. Take off the £1 tip: £3.70 – £1.00 = £2.70.
17. The fare is £5.90. The passenger gives you £10.40 so that the change is easier. How much change do you give?
Answer: C. £4.50. £10.40 – £5.90 = £4.50. Check: £5.90 + £4.50 = £10.40.
18. 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?
Answer: D. 5 coins. £2 + £2 + 50p + 20p + 10p = £4.80. That is 5 coins.
19. Three passengers share a fare of £24.60 equally. How much does each one pay?
Answer: D. £8.20. £24.60 ÷ 3 = £8.20. Check: 3 × £8.20 = £24.60.
20. Four friends share a fare of £31.00 equally. How much does each one pay?
Answer: C. £7.75. £31.00 ÷ 4 = £7.75. Check: 4 × £7.75 = £31.00.
21. The fare is £13.20. One passenger gives you £10 and the other gives you £5. How much change do you give in total?
Answer: A. £1.80. £10 + £5 = £15.00. £15.00 – £13.20 = £1.80.
22. 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?
Answer: D. 50p. The correct change is £20.00 – £14.50 = £5.50. You gave £5.00, so you still owe 50p.
Journey times and the 24-hour clock11 questions
23. You drive 12 miles at an average speed of 24 mph. How long does the journey take?
Answer: B. 30 minutes. Time = distance ÷ speed. 12 ÷ 24 = 0.5 hours, which is 30 minutes.
24. You drive 45 miles at an average speed of 30 mph. How long does the journey take?
Answer: 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.
25. You drive 8 miles at an average speed of 20 mph. How long does the journey take?
Answer: A. 24 minutes. 8 ÷ 20 = 0.4 hours. 0.4 × 60 = 24 minutes.
26. You drive for 36 minutes at an average speed of 30 mph. How far do you travel?
Answer: C. 18 miles. 36 minutes is 0.6 of an hour. 0.6 × 30 = 18 miles.
27. You leave at 14:35. The journey takes 50 minutes. What time do you arrive?
Answer: D. 15:25. 14:35 + 25 minutes = 15:00. Add the other 25 minutes: 15:25.
28. You pick up a passenger at 22:30. The journey takes 1 hour 45 minutes. What time do you arrive?
Answer: 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.
29. 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?
Answer: C. 07:40. 25 + 5 = 30 minutes. 08:10 – 30 minutes = 07:40.
30. A passenger books a car for 7.45 pm. How is this written in the 24-hour clock?
Answer: B. 19:45. For pm times, add 12 to the hour: 7 + 12 = 19, so 7.45 pm is 19:45.
31. A booking is for 00:20. When is that?
Answer: B. 20 minutes past midnight. 00:20 in the 24-hour clock is 12.20 am: 20 minutes after midnight.
32. What is 15:05 in the 12-hour clock?
Answer: D. 3.05 pm. Take 12 away from hours after 12: 15 – 12 = 3, so 15:05 is 3.05 pm.
33. A night tariff runs from 23:00 to 06:00. Which of these start times is in the night tariff?
Answer: 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.
Earnings, fuel and percentages12 questions
34. Your operator takes 15% commission. Your fares this week total £600. How much commission do you pay?
Answer: B. £90. 10% of £600 is £60 and 5% is £30. 15% = £60 + £30 = £90. (£510 is what you keep, not the commission.)
35. You take £840 in fares in a week. You pay £120 radio rent to the operator and £95 for fuel. How much is left?
Answer: A. £625. £120 + £95 = £215. £840 – £215 = £625.
36. 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?
Answer: C. £43.50. 240 ÷ 8 = 30 litres. 30 × £1.45 = £43.50.
37. Your electric car uses 0.25 kWh for each mile. You drive 120 miles. Electricity costs 28p per kWh. What does the electricity cost?
Answer: B. £8.40. 120 × 0.25 = 30 kWh. 30 × 28p = £8.40. (£33.60 is 120 × 28p, which forgets the 0.25.)
38. The council puts up fares by 4%. A journey used to cost £12.50. What does it cost now?
Answer: D. £13.00. 1% of £12.50 is 12.5p, so 4% is 50p. £12.50 + £0.50 = £13.00.
39. A card payment company charges 1.75% of each payment. A passenger pays a £40 fare by card. What is the charge?
Answer: A. 70p. 1% of £40 is 40p. 1.75 × 40p = 70p.
40. An account customer gets 10% off. The fare is £22.00. What do they pay?
Answer: A. £19.80. 10% of £22.00 is £2.20. £22.00 – £2.20 = £19.80.
41. You earn £168 in an 8-hour shift. How much is that for each hour?
Answer: C. £21. £168 ÷ 8 = £21 an hour.
42. A fixed price job pays £45 for 30 miles. How much is that per mile?
Answer: B. £1.50. £45 ÷ 30 = £1.50 a mile.
43. The mileage reading was 45,280 at the start of your shift and 45,463 at the end. How many miles did you drive?
Answer: D. 183 miles. 45,463 – 45,280 = 183 miles.
44. An operator rounds fares up to the next 10p. The worked-out fare is £14.63. What does the passenger pay?
Answer: C. £14.70. Rounding up to the next 10p turns £14.63 into £14.70. £14.60 would be rounding down.
45. Your vehicle is licensed to carry 4 passengers. A group of 7 people want to travel together. How many vehicles do they need?
Answer: 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.
Councils that test this
- Manchester: The skills assessment tests numeracy, literacy and comprehension.
- Leeds: Fares are part of the professional standards module, and Leeds checks maths at Entry Level 3.
- Nottingham: Numeracy is one of the five sections of the Topography Test.
- Bristol: "How to calculate change" is part of the change and road safety section; the Council's example asks for the change from £30.
Questions people ask
What maths is in the taxi knowledge test?
It depends on the council, but most numeracy questions are everyday sums: working out a fare from a tariff, adding waiting time or extras, giving change from a note, splitting a fare between passengers, and working out journey times with the 24-hour clock. Calculators are not usually allowed, so practise doing the sums on paper.
Who sets taxi fares?
For hackney carriages, the council sets the maximum fares in a table of fares (Local Government (Miscellaneous Provisions) Act 1976, section 65). The meter must be set to that table. Private hire fares are not set by the council in the same way. They are agreed with the passenger in advance, or set by the operator when the booking is made.
What is a flag fall on a taxi meter?
The flag fall is the starting charge on the meter when the hire begins. It often covers a first short distance, such as the first half mile. After that, the meter adds a set amount for each extra part of a mile, and for waiting time.
Do I need to know my council's fares for the test?
Some councils ask hackney carriage drivers about their own table of fares, so read it before the test. The tariffs on this page are made up for practice. Check your council's current table of fares, as councils change them from time to time.
Other core topics
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.
- 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.
- 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.
- 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.
Councils update their tests and policies, often yearly. If something here no longer matches your council's guidance, the council is right; please tell us so we can fix it.