Best Buys and Currency Conversion
Best buys questions ask you to decide which pack, deal or offer gives the most for your money, and in Edexcel IGCSE Maths they sit alongside currency conversion in the same money topic. On this page you will learn to compare prices using unit costs, convert between currencies in both directions, and deal with exchange fees, commission and round trips. Worked examples build the method step by step, then the auto-marked practice questions below give you unlimited fresh questions with instant feedback.
What Are Best Buys?
A best buys question gives you two or more packs of the same product in different sizes and asks which one is better value for money. The bigger pack often looks cheaper, but the only fair test is the unit price: what one unit of the product actually costs. Shops print unit prices on shelf labels for exactly this reason.
- Choose a unit that every pack can share: one item, 100 g, 100 ml, one litre or one metre.
- Divide each price by the number of units in that pack to get its unit price.
- Compare the unit prices. The lower unit price is the better value.
Working in pence (or cents) keeps the division tidy. For a cost per 100 g, divide the price by the number of 100 g blocks in the pack: a 300 g pack contains 3 blocks of 100 g, so divide its price by 3.
Comparing two bottles of apple juice by cost per 100 ml
The big bottle holds more, but at 25p per 100 ml it is not the cheapest way to buy the juice. The 750 ml bottle wins at 24p per 100 ml. Never judge by pack size or headline price alone; always compare unit prices.
The cost of one unit: one item, 100 g, 100 ml or one litre. Lower unit price means better value.
Both packs must be measured in the same unit before you compare. Convert litres to ml if you need to.
Multiply by the exchange rate to buy the foreign currency; divide by the same rate to come back.
A fixed fee or a percentage commission is removed from your money before the rate is applied.
Currency Conversion in Both Directions
An exchange rate tells you how much foreign currency one unit of your own money buys. A rate of £1 = €1.15 means every pound turns into 1.15 euros. The same rate works in both directions, but the operations are opposites. Think of them as two separate tools, and pick the one that matches the direction of your journey:
The two-way conversion machine for £1 = €1.15
A quick sense check saves marks: 1.15 euros is worth the same as 1 pound, so the euro figure should always be the bigger number when the rate is above 1. If your answer moved the wrong way, you picked the wrong tool.
Exchange Fees, Commission and Round Trips
Real currency desks are not free. Exam questions copy the three charges you meet at an airport kiosk:
- Fixed fee: a flat charge, such as £5, is taken off your money first. Only what is left gets converted.
- Percentage commission: the desk keeps a percentage, say 2%, of your money, then converts the remaining 98%.
- Round trip: the desk sells you euros at one rate but buys them back at a worse rate. Converting money there and straight back always loses you some of it.
What a fee and a round trip do to your money
When two offers are compared, a better headline rate does not guarantee more money: a £10 fee can wipe out the advantage of a slightly higher rate. Work each offer out to the end before you decide, exactly like a best buys question, and compare the final amounts.
Worked Examples
💡 Example 1: Which Pack Is the Best Buy?
A pack of 8 felt-tip pens costs £2.40. A pack of 12 of the same pens costs £3.24. Which pack is better value?
Work in pence and compare the cost of one pen:
\[ \begin{array}{rcl} \text{Pack of 8, per pen} &=& 240\text{p} \div 8 \\ &=& 30\text{p} \\ \text{Pack of 12, per pen} &=& 324\text{p} \div 12 \\ &=& 27\text{p} \end{array} \]The pack of 12 is better value.
What's happening?
Split each price equally between the pens in the pack: divide by 8 for the first pack and by 12 for the second.
27p per pen beats 30p per pen: the lower cost per item wins.
💡 Example 2: Pounds into Rand
Convert £260 into South African rand. The exchange rate is £1 = R23.40.
So £260 buys R6084.
What's happening?
You are going into the foreign currency, so you multiply by the rate.
Sense check: each pound is worth over 23 rand, so the rand figure must be much bigger than 260. It is.
💡 Example 3: Euros back into Pounds
Amara returns from holiday with €333.50. The exchange rate is £1 = €1.15. How many pounds does she get?
She receives £290.
What's happening?
She is coming back to her own currency, so she divides by the same rate.
Sense check: euros are worth less than pounds here, so the pound figure must be smaller than 333.50. It is.
💡 Example 4: Commission First, Then Convert
A currency kiosk charges 2% commission, then converts what is left at £1 = €1.15. How many euros does a customer receive for £400?
The customer receives €450.80.
What's happening?
The kiosk takes its cut before converting, so only £392 is exchanged.
Converting all £400 and then taking 2% of the euros gives the same answer here, but follow the order in the question: fee first, then convert.
💡 Example 5: The Round Trip That Loses Money
A bank sells euros at £1 = €1.20 and buys euros back at €1 = £0.78. Priya changes £250 into euros, then her trip is cancelled and she immediately changes all the euros back into pounds. How much money does she lose?
Priya loses £16.
What's happening?
Both directions are quoted as a multiplication here: the bank sells euros at 1.20 per pound but only pays 0.78 of a pound for each euro when buying them back.
A fair buy-back rate would be \(1 \div 1.20\), which is about £0.83 per euro. The gap between 0.83 and 0.78 is the bank's profit, and it is exactly where Priya's £16 went.
🔑 Key Points
- Better value means the lower unit price, not the bigger pack or the smaller price tag.
- Pick a shared unit (one item, 100 g, 100 ml, one litre) and divide each price by its number of units.
- Multiply by the exchange rate to enter the foreign currency; divide by it to come back.
- Fees and commission come off your money before the rate is applied.
- Compare full offers to the end: a better rate can still lose to a smaller fee.
⚠️ Common Pitfalls
- Assuming the biggest pack is automatically the best buy. Check the unit price; it is often not.
- Multiplying when you should divide (or the reverse). Sense check which side of the rate should be the bigger number.
- Comparing packs in different units, such as pence per gram against pounds per kilogram.
- Applying commission after converting when the question takes it first. Follow the order in the question.
- Rounding money answers too early. Keep exact values and give final answers to 2 decimal places.