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# Reverse percentages
- URL: https://www.esheets.io/reverse-percentages/
- Published: 2025-04-26T12:48:27.000Z
- Updated: 2026-06-21T16:47:06.000Z
- Author: Richard Linnington
- Tags: Maths, Number

Reverse percentage calculations are super useful when you’re trying to work backwards from a total that **already includes** a percentage increase or decrease — like figuring out the original price of an item before a sale, or working out the starting population before a percentage growth. It’s like being a maths detective, uncovering what the number was **before** the change happened! [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise reverse percentages with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Identifying the final value after a percentage change.
- Using the correct percentage multiplier.
- Working backwards to the original amount.
- Checking whether the original amount should be larger or smaller.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

## Topic guide

### What this worksheet practises

This worksheet practises calculating the original amount before a percentage increase or decrease was applied. This is known as reverse percentages. It is a common challenge because you cannot simply subtract the percentage from the final amount.

### Key method

To find the original amount, you must work backwards using the percentage multiplier.

1. Determine the multiplier for the percentage change. (For example, a 20% increase gives a multiplier of 1.20\. A 15% decrease gives a multiplier of 0.85).
2. Set up the equation: **Original Amount × Multiplier = New Amount**.
3. Rearrange to find the original amount: **Original Amount = New Amount ÷ Multiplier**.

### Worked example

**A jacket is in a sale with 20% off. The sale price is £64\. Calculate the original price.**

Step 1: Find the multiplier for a 20% decrease. 100% − 20% = 80%, which is 0.80 as a decimal multiplier.

Step 2: Write the equation. Original × 0.80 = 64

Step 3: Divide to find the original amount.

Original = 64 ÷ 0.80 = £80

The original price was £80.

### Common mistakes to avoid

A very common error is trying to find 20% of the *sale price* and adding it back on (e.g., finding 20% of £64, which is £12.80, and adding it to make £76.80). This is incorrect because the original 20% reduction was calculated based on the starting price, not the sale price.