0580

Percentages Toolkit

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

Divide by the original amount, not the new one: the change goes on top and the starting value underneath, so 40 rising to 50 is 10 ÷ 40. Read which value came first before writing the fraction, because profit, loss and "percentage increase" all use the same rule and only differ in which number is the original.

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