Reverse percentages and percentage change are essential components of GCSE Maths and are rigorously assessed by major UK exam boards such as AQA, Edexcel, and OCR. While these concepts may seem straightforward at first glance, they often lead to confusion, especially when students must work backwards or interpret questions embedded in word problems. This comprehensive guide not only explains these topics clearly but also provides practical strategies, real-world examples, and exam-style questions to help you succeed with confidence.

Master GCSE percentage skills with guided help

🔹 Understanding Percentage Change

Percentage change refers to the extent of increase or decrease in a quantity compared to its original value. It’s a useful concept not just in exams but also in day-to-day scenarios such as price fluctuations, profit/loss calculations, and more. Understanding how to calculate percentage change equips students with practical numeracy skills.

✅ Percentage Change Formula:

Percentage Change = (change in value/original value)100

📌 Example 1:

An item’s price increases from £60 to £72: (72-60)/60 * 100 = (12/60)100 = 20% increase

📌 Example 2:

A phone’s price drops from £900 to £765: ………

📌 Example 3:

A student’s exam score improves from 40 to 50 marks: …………

📌 Real-Life Application:

If your utility bill increases from £120 to £144, the percentage increase is: (144-120)/120 * 100 = 20% increase

🟢 What Are Reverse Percentages?

Reverse percentages involve calculating the original value before a percentage increase or decrease was applied. This type of question is very common in GCSE exams and often requires a good understanding of multiplier methods and reverse operations.

These questions often begin with phrases like:

• “After a 20% increase…”
• “The current price is…”
• “Calculate the original amount…”
• “Following a 10% discount…”

✅ Strategy: Use a Multiplier

To work backwards from a percentage increase or decrease, convert the percentage into a decimal multiplier. For an increase of 20%, the final amount is 120% of the original, which is 1.2 × the original amount.

So to find the original: Original = Final/Multiplier

📌 Example 1:

A jacket costs £84 after a 20% increase. Original Price = 84/1.2 = £70

📌 Example 2:

A phone is now priced at £510 after a 15% discount. What was the original price? ………

📌 Example 3:

An item is sold for £900 after a 25% markup: Original Price = 900/1.25 = £720

📌 Reverse Depreciation Example:

A car is worth £5780 after a 15% depreciation: Original Value = 5780/0.85 = £6800

🔹 Tips for Percentage Questions in Exams

Percentage-based questions can come in various forms—from direct calculations to embedded word problems. Here are some exam-focused tips:

• Always determine whether it’s an increase or a decrease
• Use decimal multipliers rather than repeatedly calculating percentages
• Identify key figures in the problem—starting value, ending value, and rate
• Check units and context – e.g., money, weight, population
• Estimate answers before finalising to ensure logic
• Always show full working, especially in calculator papers

💡 Quick Multipliers Guide:

📑 GCSE Practice Questions:

1. After a 25% increase, a watch costs £875. What was its original price?
2. A bike worth £560 has decreased by 12%. What is its new value?
3. A house was bought for £160,000 and sold for £192,000. Calculate the percentage increase.
4. A phone depreciates by 18% and is now worth £666. Find the original price.
5. A laptop is sold for £540 after a 10% discount. What was the original price?
6. An item’s value increased by 35% to £945. What was its previous value?

These examples reflect the format and difficulty of actual GCSE exam questions.

🎯 Final Revision Tips

• Memorise common percentage changes and their multipliers
• Practice identifying whether questions are direct or reverse
• Use real-world scenarios to test your skills (e.g., shopping discounts)
• Show all steps for maximum marks
• Read each question carefully, especially in multi-step problems
• Practice mixed questions to build confidence and accuracy under exam conditions

✅ Final Thoughts

Mastering reverse percentages and percentage change is essential for every GCSE Maths student. These topics not only appear in all major UK exam boards but are also crucial for understanding real-world financial literacy—whether it’s calculating discounts, estimating depreciation, or analysing data.

With the right strategies, clear formula knowledge, and plenty of practice, you can tackle even the most challenging percentage problems with confidence. Let your preparation begin today.

For structured lessons, expert-led tutorials, and interactive resources tailored to your exam board, visit GCSE Maths Tutor and elevate your skills in no time.