Reverse Percentages Lecture Notes

Introduction to Reverse Percentages

• Purpose: To find the original value after a percentage change.
• Example scenario: House price increased by 15%, new price is £207,000.

Key Concept

• Original price = 100%
• Increased price = 115% (100% + 15%)

Example 1: House Price

• Given: New price = £207,000
• Calculation:
  • Find 1%: 207,000 ÷ 115 = £1,800
  • Find original price: £1,800 × 100 = £180,000
• Conclusion: Original house price was £180,000.

Exam Strategy

• Think of the new price as 115% of the original value.
• Calculate 1% from the new price then scale up to find 100%.

Example 2: Sunglasses Discount

• Scenario: Sunglasses priced at £72 after 20% discount.
• Original Price Calculation:
  • New price = 80% of original price (100% - 20%) = 80.
  • Calculation: 72 ÷ 80 = £0.90 (1%)
  • Original price: £0.90 × 100 = £90.
• Conclusion: Original price of sunglasses was £90.

Example 3: Car Price Decrease

• Given: Car price decreased by 8%, new price = £12,880.
• Calculation:
  • New price = 92% of original price (100% - 8%).
  • 12,880 ÷ 92 = £140 (1%)
  • Original price: £140 × 100 = £14,000.
• Conclusion: Original car price was £14,000.

Different Type of Reverse Percentage Questions

• Example: Seasonal rail tickets increased by 5%, ticket cost increased by £42.50.
• Calculation:
  • 5% of original price = £42.50.
  • Find 1%: 42.50 ÷ 5 = £8.50.
  • Original price: £8.50 × 100 = £850.
• New Price Calculation:
  • New price after increase: £850 + £42.50 = £892.50.
• Conclusion: Original ticket price was £850, new price is £892.50.

Example 4: Dress Price Reduction

• Given: Dress reduced by £8.10 (18% reduction).
• Calculation:
  • 1% = 8.10 ÷ 18 = £0.45.
  • Original price: £0.45 × 100 = £45.
• Conclusion: Original price of dress was £45.

Conclusion

• Reverse percentages can be tricky, practice with exam questions is recommended.
• Use clear calculation steps for clarity in exams.