Example. A journey starts at 22:35 and lasts 2 h 48 min. Find the arrival time.

Add 2 h to get 00:35 the next day, then add 48 min: the arrival time is 01:23.

A leap year has 366 days (February has 29 days). A year is a leap year if it is divisible by 4, except century years — which must be divisible by 400. So 2000 was a leap year, but 1900 was not.

To find the time between two given times, count on from the start time to the end time. This is often easier than subtracting.

When crossing midnight, split the calculation at midnight (00:00). Count to midnight first, then from midnight onwards. This avoids errors.

Read the question carefully: is it asking for arrival time, departure time, or duration? Always check whether a dash (—) in a timetable means the bus does not stop there.

The Earth spins west to east, so places to the east see the sun rise first. Travelling east chases the sunrise into a later local time — add the difference. Travelling west chases the sunset backwards into an earlier local time — subtract the difference.

Convert both to UTC:

When subtracting hours crosses midnight, the date changes. E.g. 02:00 - 5 hours 21:00 the previous day. Always state if the date changes in your answer.

Question. A flight lands at $03:20$ (the next day) after a flight duration of $9$ hours $45$ minutes. What local time did it depart?

Every earlier example found an end time from a start, or a duration from two clock times. Here you're given the end and the duration and must find the start — subtract instead of add, and watch the date roll backwards.

Question. State, with a reason, whether each of these is a leap year: (a) $2024$, (b) $2100$, (c) $2400$.

2000 and 1900 aren't the only century years that matter — 2100 and 2400 are exactly the kind of case the "divisible by 400" exception exists for.

Question. A flight departs Cairo (UTC+2) at $23:10$ local time. The flight takes $6$ hours $50$ minutes. Find the local arrival time in Tokyo (UTC+9).

This combines two separate skills: adding a duration to a clock time (Timetables) and converting between local times via UTC (Time Zones) — always add the duration in UTC before converting to the destination's local time.

When splitting a bill and the division doesn't work exactly, state the individual share to 2 d.p. and note the rounding. The examiner expects 2 decimal places in your answer.

Students often multiply when they should divide (or vice versa). Ask yourself: "Should my answer be bigger or smaller?" If converting to a weaker currency, you should get more units.

In real life, banks give different rates for buying and selling currency. If a question gives two rates, the bank buys foreign currency at a lower rate and sells at a higher rate. Read the question carefully to pick the correct rate.

For a 25% profit, multiply CP by 1.25. For a 15% loss, multiply CP by 0.85. The multiplier is always $1\pm \frac{r}{100}$.

Monthly income: $3800

Total expenses = $1200+650+280+190+430$ = $2750

$Surplus=3800-2750=$$1050

This surplus could be saved or invested.

If total expenses > income, there is a deficit (over-spending). If income > expenses, there is a surplus.

Question. A laptop costs $780 in the US, or £650 in the UK. Using the exchange rate £1 = $1.30, which country offers the better price, and by how much (in pounds)?

Convert both prices into the same currency before comparing — exactly the "like with like" rule from best-value ratio problems, just with currencies instead of pack sizes.

Question. A shopkeeper sells a bicycle for $299, making a profit of $15\%$ on what she paid for it. Find the cost price.

Every profit/loss example above started from the cost price. Here you're given the selling price instead — this is a reverse percentage in disguise, so divide by the multiplier rather than multiplying.

Question. A water company charges $0.60 per unit for the first $20$ units used, then $0.90 per unit for every unit after that. Find the total bill for a household using $35$ units in a month.

Unlike the flat-rate electricity example above, this bill is tiered — split the usage into bands first, and apply each rate only to the units in its own band, not to the whole amount.

Question. The exchange rate is $1$ pound $=1.27$ US dollars. Convert (a) $240$ pounds to dollars, (b) $508$ dollars to pounds.

Marking. 1 mark per point. The direction check catches the commonest error — multiplying when you should divide.

Question. A train leaves at $14:37$ and arrives at $17:12$. (a) How long is the journey? (b) The distance is $310\text{km}$; find the average speed in $\text{km/h}$.

Marking. 1 mark per point. Convert minutes to a decimal fraction of an hour before dividing — using $2.35$ instead of $2.58\overline{3}$ is the standard error.

Question. Priya works $37$ hours at $\pounds 12.40$ per hour, plus $6$ hours overtime at time-and-a-half. She pays $20\%$ tax on everything above $\pounds 250$. Find her take-home pay.

Marking. 1 mark per point. Tax applies only to the amount above the threshold, not to the whole wage.

Reasoning prompt. A timetable journey crosses midnight. How can you make the elapsed time visible?

Money should normally be stated to two decimal places, but calculation values should not be rounded early.

If 1 unit of currency A buys 1.25 units of currency B, then 240 A buys $240\times 1.25=300$ B.

To reverse the conversion, divide: $300÷1.25=240$ A. Applying the published rate and its inverse should return the starting amount, apart from stated fees or rounding.