0580

Percentages Toolkit

Number

Working backwards from the new value

  • Some questions give the value after a change and ask for the value before it
  • The change applied to the original, so the original multiplied by the multiplier gives the new value
  • Rearranging, the original is the new value divided by the multiplier
  • Identify the multiplier from the percentage change described, not from the figure given

The trap

  • Applying the percentage to the new value is the common error, and it does not undo the change
    • Increasing 200 by 20% gives 240, but decreasing 240 by 20% gives 192, not 200
  • The two operations use different bases, so they are not inverses of one another
Exam tip

Write the line original × multiplier = given value before dividing — that is what keeps the division the right way up. The phrase "reverse percentage" appears in none of these 43 papers; the signal is the word original, or any request for a value before a change. Check by applying the change to your answer.

Worked example

Finding the original price

In a sale, the price of a coat is reduced by 15%. The sale price is £102. Find the original price.

Solution:

  • Removing 15% leaves 85% of the original, giving a multiplier of 0.85
  • original × 0.85 = 102
  • Divide both sides by 0.85: original = 102 ÷ 0.85
  • The original price was £120
  • Check: 15% of 120 is 18, and 120 − 18 = 102