Reverse Percentages and Finding Original Values

Introduction

• Concept of reverse percentages: Finding the original value after a percentage change.

Example 1: House Price Increase

• Given:
  • New price of house = £207,000
  • Increase = 15%
• Process:
  • Original price = 100%
  • New price = 115% of original price (100% + 15%)
  • Calculate 1%:
    • £207,000 / 115 = £1,800
  • Find original price:
    • £1,800 * 100 = £180,000
• Conclusion:
  • Original price of the house was £180,000.*

Example 2: Sunglasses Discount

• Given:
  • Sale price of sunglasses = £72
  • Discount = 20%
• Process:
  • Original price = 100%
  • Sale price = 80% of original price (100% - 20%)
  • Calculate 1%:
    • £72 / 80 = £0.90
  • Find original price:
    • £0.90 * 100 = £90
• Conclusion:
  • Original price of sunglasses was £90.*

Example 3: Car Price Decrease

• Given:
  • New price of car = £12,880
  • Decrease = 8%
• Process:
  • Original price = 100%
  • New price = 92% of original price (100% - 8%)
  • Calculate 1%:
    • £12,880 / 92 = £140
  • Find original price:
    • £140 * 100 = £14,000
• Conclusion:
  • Original price of the car was £14,000.*

Example 4: Seasonal Rail Ticket Increase

• Given:
  • Price increase = £42.50
  • Increase percentage = 5%
• Process:
  • Original price = 100%
  • Calculate 1%:
    • £42.50 / 5 = £8.50
  • Find original price:
    • £8.50 * 100 = £850
• New Price After Increase:
  • £850 * 105 = £892.50
  • Alternatively, add increase to original price:
    • £850 + £42.50 = £892.50

Example 5: Dress Price Reduction

• Given:
  • Price reduction = £8.10
  • Reduction percentage = 18%
• Process:
  • Calculate 1%:
    • £8.10 / 18 = £0.45
  • Find original price:
    • £0.45 * 100 = £45
• Conclusion:
  • Original price of the dress was £45.*

Final Remarks

• Mastering reverse percentages can be challenging.
• Practice with exam questions and check solutions to improve skills.
• Encourage likes and subscriptions for further learning.