Ratio & ProportionDeep Dive
Understanding Reverse Percentages
Part of Reverse Percentages — GCSE Mathematics
This deep dive covers Understanding Reverse Percentages within Reverse Percentages for GCSE Mathematics. Revise Reverse Percentages in Ratio & Proportion for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 3 of 5 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 3 of 5
Practice
12 questions
Recall
22 flashcards
📊 Understanding Reverse Percentages
The Logic Behind Reverse Percentages
If an item costs £72 after a 20% discount:
- The £72 represents 80% of the original price (100% - 20% = 80%)
- 80% as a decimal = 0.80
- So: Original price × 0.80 = £72
- Therefore: Original price = £72 ÷ 0.80 = £90
Step-by-Step Method
- Identify what the final amount represents
- Calculate the percentage the final amount represents
- Convert to a multiplier
- Divide the final amount by the multiplier
Common Scenarios
| Scenario | Final amount represents | Calculation |
|---|---|---|
| 20% discount | 80% of original | Final ÷ 0.80 |
| 15% increase | 115% of original | Final ÷ 1.15 |
| VAT at 20% | 120% of pre-VAT price | Final ÷ 1.20 |
| 8% decrease | 92% of original | Final ÷ 0.92 |