Ratio & ProportionDiagram

Worked Examples

Part of Reverse PercentagesGCSE Mathematics

This diagram covers Worked Examples 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 4 of 5 in this topic. Focus on the labels, the relationships between parts, and the explanation that turns the diagram into an exam-ready answer.

Topic position

Section 4 of 5

Practice

12 questions

Recall

22 flashcards

🎯 Worked Examples

Example 1: Sale Price (Decrease)

Problem: Jake pays £72 for a jacket with 20% off. What was the original price?

Step 1: £72 is the price after 20% off

Step 2: So £72 represents 80% of the original (100% - 20%)

Step 3: Multiplier = 0.80

Step 4: Original price = £72 ÷ 0.80 = £90

Check: £90 × 0.80 = £72 ✓

Example 2: After VAT (Increase)

Problem: The total cost including 20% VAT is £96. What was the price before VAT?

Step 1: £96 is the price after 20% VAT was added

Step 2: So £96 represents 120% of the pre-VAT price (100% + 20%)

Step 3: Multiplier = 1.20

Step 4: Pre-VAT price = £96 ÷ 1.20 = £80

Check: £80 × 1.20 = £96 ✓

Example 3: After Growth (Increase)

Problem: A population is now 5,400 after growing by 8%. What was the original population?

Step 1: 5,400 is the population after 8% growth

Step 2: So 5,400 represents 108% of the original (100% + 8%)

Step 3: Multiplier = 1.08

Step 4: Original population = 5,400 ÷ 1.08 = 5,000

Check: 5,000 × 1.08 = 5,400 ✓

Keep building this topic

Read this section alongside the surrounding pages in Reverse Percentages. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Reverse Percentages

A price after a 20% increase is £120. Which calculation finds the ORIGINAL price?

  • A. £120 × 1.20
  • B. £120 ÷ 1.20
  • C. £120 × 0.80
  • D. £120 - 20
1 markfoundation

A TV costs £360 after a 10% increase. A student says: 'The original price was £360 - 10% = £360 - £36 = £324.' Explain the error in the student's method. What is the correct original price?

2 marksstandard

Quick Recall Flashcards

What is a reverse percentage?
Finding the original amount before a percentage change was applied
Give three examples of when you'd use reverse percentages
Finding original prices before sales, pre-tax amounts, original values before depreciation

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