EDEXCEL GCSE HIGHER MATHS - What is Reverse Percentages and Their Calculations

Reverse Percentages

Reverse percentages are used to find the original value of something when you know a percentage of it. This is often used in situations where a price has been increased or decreased by a certain percentage, and you want to find the original price.

Understanding the Concept:

Imagine you have a product that costs £100, and it's been increased by 20%. To find the new price, you would calculate 20% of £100 (which is £20) and add it to the original price, giving you £120.

Now, imagine you only know the new price (£120) and the percentage increase (20%). To find the original price, you need to use reverse percentages.

How to Calculate Reverse Percentages:

1. Represent the original price: Let 'x' be the original price.
2. Write the percentage increase/decrease as a decimal: For a 20% increase, the decimal is 1.20 (1 + 0.20). For a 20% decrease, the decimal is 0.80 (1 - 0.20).
3. Set up an equation: Multiply the original price (x) by the decimal representing the percentage change, and equate it to the final price. For example, if the final price is £120 and the percentage increase is 20%, the equation would be: 1.20x = 120.
4. Solve for x: Divide both sides of the equation by the decimal representing the percentage change. In our example, divide both sides by 1.20: x = 120 / 1.20 = 100.

Example:

A shop reduces the price of a dress by 15%. The sale price is £42.50. What was the original price?

1. Represent the original price: Let 'x' be the original price.
2. Write the percentage decrease as a decimal: The decimal is 0.85 (1 - 0.15).
3. Set up an equation: 0.85x = 42.50
4. Solve for x: x = 42.50 / 0.85 = 50

Therefore, the original price of the dress was £50.

Key Points:

• Increase: Add the percentage increase to 100% and convert to a decimal.
• Decrease: Subtract the percentage decrease from 100% and convert to a decimal.
• Understanding the equation: The equation represents the relationship between the original price, the percentage change, and the final price.

Practice Questions:

1. A car was sold for £12,000 after a 10% discount. What was the original price?
2. A company's profit increased by 15% this year. If the profit last year was £200,000, what is the profit this year?
3. A house price has increased by 25% since 2010. If the house currently costs £300,000, what was the price in 2010?

By understanding reverse percentages, you can solve various problems involving price changes, discounts, and percentage increases or decreases.