EDEXCEL GCSE FOUNDATION MATHS - What is Reverse Percentages

Edexcel GCSE Foundation Maths: Reverse Percentages

Reverse percentages involve finding the original value before a percentage increase or decrease was applied.

Understanding the Concept

Imagine you have a shirt that was discounted by 20% and now costs £24. You want to know the original price. This is a reverse percentage problem.

Steps to Solve Reverse Percentage Problems

1. Identify the Percentage Change: Determine whether the price increased or decreased and by what percentage. In our example, the price decreased by 20%.
2. Calculate the Remaining Percentage: Subtract the percentage change from 100%. In our example, 100% - 20% = 80%. This means the final price (£24) represents 80% of the original price.
3. Set up a Proportion: Write a proportion to represent the relationship between the percentage and the price.
   • 80% / 100% = £24 / Original Price
4. Solve for the Original Price: Cross-multiply and solve the equation.
   • 80% * Original Price = 100% * £24
   • Original Price = (100% * £24) / 80%
   • Original Price = £30

Example

A car's price increased by 15% to £13,800. Find the original price.

1. Percentage Change: Increased by 15%
2. Remaining Percentage: 100% + 15% = 115%
3. Proportion: 115% / 100% = £13,800 / Original Price
4. Solve:
   • 115% * Original Price = 100% * £13,800
   • Original Price = (100% * £13,800) / 115%
   • Original Price = £12,000

Key Points to Remember

• Percentage Increase: Add the percentage to 100% to find the remaining percentage.
• Percentage Decrease: Subtract the percentage from 100% to find the remaining percentage.
• Proportion: Use a proportion to relate the percentage and the known value to the unknown original value.

Practice Problems

1. A jacket was discounted by 30% and now costs £56. What was the original price?
2. A house price increased by 25% to £250,000. What was the original price?

By practicing these steps and working through problems, you'll master reverse percentage calculations for your Edexcel GCSE Foundation Maths exam.