MathematicsExam code: 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
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