Mathematics (Core)Exam code: 0580
Percentages
Number
Measuring the change
- The change is measured against the starting value, never against the final one
- Percentage change = (change ÷ original) × 100, where the change is the new value minus the old
- A positive result is an increase and a negative result is a decrease
- Dividing the new value by the old gives the multiplier directly, and reading it back gives the same answer
- A multiplier of 1.2 is a 20% increase, and 0.75 is a 25% decrease
Profit and loss
- Goods are bought at a cost price and sold at a selling price, and the same formula applies with cost price as the original
- A selling price above the cost price is a percentage profit, and below it a percentage loss
- Checking the direction against common sense catches a sign error: selling for less than was paid cannot be a profit
Exam tip
Finish at the percentage change
Going from 80 to 92, the fraction 12 ÷ 80 = 0.15 and the line 92 ÷ 80 × 100 = 115 each earn the method mark, but the answer mark is for 15 alone. Multiply the fraction by 100, or take 100 off the 115, before you write the answer. A fall works the same way: 41 ÷ 50 × 100 = 82 is a decrease of 18%, not 82%.
Worked example
Percentage loss on a sale
An item bought for £120 is later sold for £90. Find the percentage loss.
Solution:
- The change is 90 − 120 = −£30
- Divide by the cost price, which is the original value: −30 ÷ 120 = −0.25
- Multiply by 100 to get −25
- The negative sign shows a decrease, so this is a 25% loss