Exchange Rate Problems –

Exchange rate problems appear regularly on GCSE Maths papers and test your ability to convert between currencies using multiplication and division. These questions are set in real-world contexts such as holiday money, online purchases and international trade. At Foundation tier you will convert between two currencies using a given rate. At Higher tier you may encounter buying and selling rates, commission charges and multi-step problems involving more than two currencies. This guide walks you through the key methods with worked examples at every level.

What Are Exchange Rate Problems?

An exchange rate tells you how much of one currency you get for one unit of another currency. For example, if £1 = €1.15, then for every pound you exchange, you receive 1.15 euros.

Key Formulas

When a question gives buying and selling rates, the buying rate (what the bureau gives you when you buy foreign currency) is lower than the selling rate (what the bureau charges when you sell foreign currency back). The bureau profits from the difference.

Step-by-Step Method

1. Identify the exchange rate given in the question and note which direction the conversion goes.
2. Decide whether to multiply or divide. Going from pounds to a foreign currency — multiply. Going from a foreign currency back to pounds — divide.
3. Perform the calculation carefully, keeping at least two decimal places for currency.
4. Round appropriately — currency answers are usually given to two decimal places (nearest penny or cent).
5. Check reasonableness — if you exchange £100 at a rate of 1.15, you should get more than 100 euros.

Worked Example 1 — Foundation Level

Question: The exchange rate is £1 = $1.25. Convert £360 into dollars.

Working:

Amount in dollars = 360 x 1.25 = $450

Answer: £360 = $450

Worked Example 2 — Higher Level

Question: Priya exchanges £500 into euros at a rate of £1 = €1.16. She spends €412 on holiday. When she returns, the exchange rate is £1 = €1.12. How many pounds does she get back?

Working:

Step 1: Convert £500 to euros: 500 x 1.16 = €580

Step 2: Euros remaining after spending: 580 - 412 = €168

Step 3: Convert €168 back to pounds: 168 / 1.12 = £150

Answer: Priya receives £150 when she converts her remaining euros.

Worked Example 3 — Exam Style

Question: A bureau de change offers these rates: Buy rate: £1 = €1.10. Sell rate: £1 = €1.20. Javed buys €660 for his trip. How many pounds does it cost him?

Working:

When Javed buys euros, the bureau uses the sell rate (the bureau sells euros to him at the higher rate).

Pounds needed = 660 / 1.20 = £550

Note: The bureau profits by selling euros at a higher rate than it buys them back.

Answer: It costs Javed £550 to buy €660.

Common Mistakes

• Multiplying when you should divide (or vice versa). Converting to a foreign currency usually means multiplying. Converting back to pounds means dividing. Always check which direction the rate is given.
• Using the wrong rate in buy/sell problems. The bureau sells foreign currency to you at the less favourable rate for you. Read the question carefully to see which rate applies.
• Rounding too early. Keep full decimal precision during intermediate steps and only round the final answer to 2 decimal places.

Exam Tips

• Write down the exchange rate and label which currency is which. This avoids confusion in multi-step problems.
• If the answer seems too large or too small, you have probably multiplied instead of divided (or the reverse). Use common sense to check.
• On AQA and Edexcel papers, expect 3- to 5-mark currency questions that involve spending, converting back, and comparing costs.

Practice Questions

Q1 (Foundation): The exchange rate is £1 = ¥155. Convert £80 to Japanese yen.

Q2 (Foundation): The exchange rate is £1 = $1.30. How many pounds is $520?

Q3 (Higher): Emma exchanges £400 to euros at £1 = €1.14. She spends €350. She converts the rest back at £1 = €1.10. How much does she get back in pounds?

Practise exchange rate problems with instant feedback free on GCSEMathsAI.

Related Topics

• Ratio Basics and Sharing
• Percentage of an Amount
• Unit Conversions

Summary

• An exchange rate tells you how much of one currency equals one unit of another.
• Multiply to convert from pounds to a foreign currency; divide to convert back.
• Buy and sell rates differ — the bureau always takes a margin that is less favourable to you.
• Round currency answers to two decimal places (nearest penny or cent).
• In multi-step problems, work through each conversion one stage at a time and keep full precision until the final answer.
• Always check your answer is reasonable given the exchange rate.