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Reverse Percentages in GCSE Maths: How to Find the Original Price After a Discount

Updated: Jul 17


If you've ever looked at a reverse percentages question and thought, "Where do I even start?", you're not alone.

Reverse percentages are one of the most common topics students struggle with in GCSE Maths because you're working backwards from the final amount to find the original value.

In this example, we look at a classic GCSE Foundation question involving a discount and show exactly how to solve it step by step.


🎥 Watch the Video Explanation

Reverse Percentages Guide

Prefer to watch rather than read? Check out our quick TikTok walkthrough of this reverse percentages question:


The Question

A camera is reduced by 12% and now costs £123.50.How much did it cost originally?

This is a reverse percentage problem because we're given the final price after the discount and need to work backwards to find the original price.


Step 1: Work Out What Percentage Remains

The camera has been reduced by 12%, so the new price no longer represents 100% of the original value.

Instead:

100% − 12% = 88%

This means that £123.50 represents 88% of the original price.


Step 2: Find 1%


To work backwards, divide the current price by 88:

1% = £123.50 ÷ 88 = £1.4034...


Step 3: Find 100%


Now multiply by 100 to find the original price:

100% = £1.4034... × 100 = £140.34

Therefore, the original price of the camera was:

£140.34

If the question asks for the answer to the nearest whole number, the answer would be:

£140

The Faster GCSE Method

Many students prefer using the multiplier method because it is quicker and particularly useful in exam conditions.

Since 88% = 0.88, we can write:

0.88x = 123.50

Now divide both sides by 0.88:

x = 123.50 ÷ 0.88 = 140.34

Exactly the same answer, just with fewer steps.

Common Mistake to Avoid

A very common mistake is calculating:

£123.50 × 1.12

Unfortunately, this doesn't work.

Adding 12% onto the discounted price is not the same as reversing a 12% reduction because the percentages are being calculated from different starting amounts.

When working with reverse percentages, always ask yourself:

"What percentage does the current amount represent?"

Once you've identified that percentage, the rest of the question becomes much easier.

Why Reverse Percentages Matter

Reverse percentages appear regularly in:

  • GCSE Foundation Maths

  • GCSE Higher Maths

  • Functional Skills Maths

  • Apprenticeship assessments

  • Business and finance calculations

You might see questions involving:

  • Discounts

  • VAT

  • Salary increases

  • Inflation

  • Population growth

  • Interest rates

Mastering reverse percentages will help across multiple areas of mathematics and real-life problem solving.


📝 Practice Questions

Think you've mastered reverse percentages? Have a go at these GCSE-style questions before checking your answers.


A jacket is reduced by 20% and now costs £64. How much did it cost originally?

  • A) £76.80

  • B) £80

  • C) £84

  • D) £96


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