IGCSE Maths · Number · Core & Extended

Time and Money: Clocks, Timetables and Currency

This closes out the Number unit — and it’s identical for Core and Extended. Nothing here is conceptually hard, but it’s easy to lose marks through small slips (treating 3.5 hours as 3 hours 50 minutes, mixing up am/pm, forgetting a currency conversion goes both ways). This note is about eliminating exactly those slips.

Why this matters Catching a flight, reading a bus timetable, splitting a bill, converting your spending money before a trip abroad — time and money are the two things almost everyone calculates by hand most often in real life, calculator or not.

1. Time Unit Conversions

UnitEquivalent
1 minute60 seconds
1 hour60 minutes
1 day24 hours
1 week7 days
1 year365 days (12 months)
Worked examples Convert 2.5 hours into hours and minutes.
0.5 hours = 0.5 × 60 = 30 minutes → 2 hours 30 minutes

Convert 3 days into hours.
3 × 24 = 72 hours

Convert 320 seconds into minutes and seconds.
320 ÷ 60 = 5 remainder 20 → 5 minutes 20 seconds
Try it — Time Conversions
  1. Convert 4.25 hours into hours and minutes.
  2. Convert 150 minutes into hours and minutes.
  3. Convert 5 weeks into days.
  4. Convert 500 seconds into minutes and seconds.
Show answers
  1. 4 hours 15 minutes
  2. 2 hours 30 minutes
  3. 35 days
  4. 8 minutes 20 seconds

2. The 24-Hour and 12-Hour Clock

The 24-hour clock avoids any am/pm confusion — it always uses 4 digits, counting from 0000 (midnight) to 2359 (one minute before midnight).

Worked examples Write 3:15 a.m. in 24-hour time.
Morning times before noon keep the same hour: 0315

Write 3:15 p.m. in 24-hour time.
Add 12 to the hour for afternoon/evening times: 3 + 12 = 15 → 1515

Write 1847 in 12-hour time.
1847 is after 1200, so subtract 12: 18 − 12 = 6 → 6:47 p.m.
Try it — Clock Conversions
  1. Write 9:05 a.m. in 24-hour time.
  2. Write 11:40 p.m. in 24-hour time.
  3. Write 0630 in 12-hour time.
  4. Write 2058 in 12-hour time.
Show answers
  1. 0905
  2. 2340
  3. 6:30 a.m.
  4. 8:58 p.m.

3. Calculating Durations

The safest method: convert both times to 24-hour clock, then count forward in convenient chunks (to the next whole hour, then the remaining minutes) rather than subtracting like ordinary decimals.

Worked example A flight departs at 0940 and arrives at 1325 the same day. Find the flight duration.
0940 to 1000 = 20 minutes
1000 to 1300 = 3 hours
1300 to 1325 = 25 minutes
Total: 20 min + 3 h + 25 min = 3 hours 45 minutes
Worked example — crossing midnight A concert starts at 2230 and lasts 3 hours 50 minutes. Find the finish time.
2230 + 1 hour 30 minutes = 0000 (midnight)
Remaining time: 3 h 50 min − 1 h 30 min = 2 h 20 min
0000 + 2 h 20 min = 0220 (the next day)
Try it — Duration Calculations
  1. A train departs at 1145 and arrives at 1610. Find the journey duration.
  2. A film starts at 1950 and runs for 2 hours 35 minutes. Find the finish time.
  3. A flight departs at 2305 and lasts 6 hours 40 minutes. Find the arrival time (and note it lands the next day).
Show answers
  1. 1145 to 1200 = 15 min; 1200 to 1600 = 4 h; 1600 to 1610 = 10 min. Total = 4 h 25 min.
  2. 1950 + 10 min = 2000; remaining 2 h 25 min; 2000 + 2 h 25 min = 2225.
  3. 2305 + 55 min = 0000; remaining 6h40min − 55min = 5h45min; 0000 + 5h45min = 0545 the next day.

4. Reading Timetables

Timetable questions usually ask for a journey time, a waiting time, or which service to catch to arrive by a certain time. Read carefully — every column is a different bus or train.

Sample timetable
StopBus 1Bus 2Bus 3
Market Square071507450820
Library072807580833
Hospital074108110846
Station075508250900
A student needs to be at the Hospital by 0815. Which bus should they catch from Market Square, and how long is the ride from Market Square to Hospital?
Bus 2 reaches Hospital at 0811, in time. From Market Square (0745) to Hospital (0811) is 26 minutes.
Try it — Timetables (use the table above)
  1. How long does Bus 1 take from Market Square to the Station?
  2. A passenger arrives at the Library at 0800. How long must they wait for the next bus?
  3. Which bus should be caught from the Library to arrive at the Station no later than 0830?
Show answers
  1. 0715 to 0755 = 40 minutes
  2. The next bus after 0800 at the Library is Bus 3 at 0833 — a wait of 33 minutes.
  3. Bus 2 (Library 0758 → Station 0825)

5. Time Zones and Local Time

Different places on Earth use different local times, usually described as an offset from a reference time (such as GMT). To find the time somewhere else, add or subtract the difference in offsets.

Worked example City A is GMT+5. City B is GMT−3. When it is 1400 in City A, what time is it in City B?
Difference between the two zones: 5 − (−3) = 8 hours (City A is 8 hours ahead of City B)
1400 − 8 hours = 0600 (same day, in City B)
Try it — Time Zones
  1. City X is GMT+2. City Y is GMT+9. When it is 1000 in City X, what time is it in City Y?
  2. City P is GMT−4. City Q is GMT+1. When it is 2200 in City Q, what time is it in City P (careful — this one crosses to the previous day)?
Show answers
  1. Difference = 9 − 2 = 7 hours ahead. 1000 + 7 = 1700 in City Y.
  2. Difference = 1 − (−4) = 5 hours; City P is behind. 2200 − 5 = 1700, same day, in City P.

6. Calculating with Money

Money calculations follow ordinary decimal rules — the only extra care needed is rounding sensibly to the nearest smallest unit of currency (usually 2 decimal places), and keeping track of totals carefully when several items are involved.

Worked example A shopping bill has three items: $4.65, $12.20, and $0.85. Find the total, and the change from a $20 note.
Total: 4.65 + 12.20 + 0.85 = $17.70
Change: 20.00 − 17.70 = $2.30
Try it — Money Arithmetic
  1. Find the total of $6.40, $3.15, and $9.99.
  2. Find the change from a $50 note after spending $34.60.
  3. Three friends split a bill of $58.50 equally. How much does each pay?
Show answers
  1. $19.54
  2. $15.40
  3. $19.50

7. Converting Between Currencies

Multiply to convert from the base currency to the foreign currency; divide to convert back.

Worked example The exchange rate is 1 GBP = 104 INR. Convert 75 GBP to INR, and separately convert 5,200 INR to GBP.
75 × 104 = 7,800 INR
5,200 ÷ 104 = 50 GBP
Try it — Currency Conversion
  1. The exchange rate is 1 USD = 83 INR. Convert 120 USD to INR.
  2. Using the same rate, convert 6,225 INR to USD.
  3. The exchange rate is 1 EUR = 1.08 USD. A jacket costs 45 EUR. Find its price in USD.
Show answers
  1. 120 × 83 = 9,960 INR
  2. 6,225 ÷ 83 = 75 USD
  3. 45 × 1.08 = $48.60
Common mistakes to watch for
  • Treating time as an ordinary decimal — 3.5 hours is 3 hours 30 minutes, not 3 hours 50 minutes.
  • Mixing up am and pm when converting 12-hour to 24-hour time, especially around 12 noon and 12 midnight.
  • Subtracting times directly across midnight without adjusting for the day change.
  • Converting currency the wrong way around — always check which direction the question wants (multiply to go from base to foreign, divide to go back).
  • Leaving a money answer with more than 2 decimal places, or rounding incorrectly and losing a cent along the way.

8. Quick-Fire Challenge Round

True or False?
  1. 1.5 hours is the same as 1 hour 50 minutes.
  2. 1200 in 24-hour time is noon.
  3. 0000 in 24-hour time is midnight.
  4. To convert from a foreign currency back to the base currency, you divide by the exchange rate.
Show answers
  1. False — 1.5 hours is 1 hour 30 minutes (0.5 × 60 = 30, not 50).
  2. True.
  3. True.
  4. True.
Spot the Error
  1. “7:20 p.m. in 24-hour time is 0720.”
  2. “A film starts at 2140 and lasts 2.5 hours, so it ends at 2140 + 2.50 = 2390.”
  3. “To convert 90 USD to INR at a rate of 1 USD = 83 INR, I divided: 90 ÷ 83.”
Show answers
  1. 7:20 p.m. is after noon, so 12 must be added: 0720 is actually 7:20 a.m. — the correct answer is 1920.
  2. Time can’t be added like a decimal — 2.5 hours is 2 hours 30 minutes; also, “2390” isn’t a valid 24-hour time at all (minutes can’t exceed 59). Correct: 2140 + 2h30min = 0010 the next day.
  3. To convert from the base currency (USD) to the foreign currency (INR), multiply, not divide: 90 × 83 = 7,470 INR.

9. Mixed Practice — Bringing It All Together

  1. Convert 3 hours 40 minutes into hours, as a decimal.
  2. Write 1608 in 12-hour time.
  3. A bus departs at 0855 and arrives at 1020. Find the journey duration.
  4. Find the total of $2.75, $8.30, and $14.99, and the change from $30.
  5. The exchange rate is 1 GBP = 95 INR. Convert 60 GBP to INR.
Show answers
  1. 3 h 40 min = 3 + 40/60 = 3.67 hours (2 d.p.)
  2. 4:08 p.m.
  3. 1 hour 25 minutes
  4. Total = $26.04; change = $3.96
  5. 5,700 INR

Practice at Home

A large set to close out the whole Number unit — take it steadily.

Part A — Time unit conversions
  1. Convert 5.75 hours into hours and minutes.
  2. Convert 4 days into hours.
  3. Convert 275 seconds into minutes and seconds.
  4. Convert 3 hours 15 minutes into a decimal number of hours.
Part B — 24-hour and 12-hour clock
  1. Write 6:50 a.m. in 24-hour time.
  2. Write 10:05 p.m. in 24-hour time.
  3. Write 1310 in 12-hour time.
  4. Write 0025 in 12-hour time.
Part C — Duration calculations
  1. A meeting starts at 0930 and ends at 1215. Find its duration.
  2. A train journey starts at 1745 and takes 5 hours 30 minutes. Find the arrival time (state if it’s the next day).
  3. A movie ends at 2320, having run for 2 hours 45 minutes. Find the start time.
Part D — Timetables and time zones
  1. Using the sample timetable in Section 4, how long does Bus 3 take from Market Square to the Station?
  2. Using the same timetable, a passenger reaches the Hospital at 0805. How long must they wait for the next bus at that stop?
  3. City M is GMT+3. City N is GMT−6. When it is 0900 in City M, what time is it in City N?
Part E — Money and currency
  1. Find the total of $5.50, $11.25, and $3.80.
  2. Find the change from a $100 note after spending $67.35.
  3. Four friends split a restaurant bill of $86.40 equally. How much does each pay?
  4. The exchange rate is 1 USD = 83 INR. Convert 250 USD to INR, and separately convert 2,490 INR to USD.
Part F — Applied / challenge
  1. A flight departs Location A at 2340 local time and lands 8 hours 20 minutes later. Location B is 3 hours behind Location A. Find the local arrival time in Location B.
  2. A shop offers a 15% discount, then charges a currency conversion at 1 USD = 83 INR. An item is priced at $60 before the discount. Find the final price in INR after the discount is applied.
  3. Explain, using an example, why 2.75 hours is not the same as “2 hours 75 minutes” — and show what 2.75 hours actually equals in hours and minutes.

Key Vocabulary Recap

24-hour clock — time written as 4 digits, from 0000 to 2359
Duration — the length of time between a start and an end
Timetable — a schedule showing departure/arrival times for a service
Time zone — a region using the same local time, usually described as an offset from GMT
Exchange rate — the value of one currency in terms of another

Syllabus Reference

This note covers Cambridge IGCSE Mathematics (0580) sections C1.15 and C1.16 (Core subject content) and E1.15 and E1.16 (Extended subject content) — Time, and Money. As with Ratio, Proportion and Rates, the wording of these sections is identical for both tiers. This is the final note in the Number unit — Algebra and graphs is next.

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