Reverse Percentages Practice Test Worksheets
Build confidence with printable reverse percentages worksheets and focused maths practice tests. Students learn to find original amounts after percentage increases, decreases, and discounts while improving their accuracy with multi-step percentage word problems.
For students who understand percentages, but need practice turning word problems into reliable reverse calculations.
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The Rules Every Reverse Percentage Question Uses
These worksheets use several word-problem styles, but each one depends on identifying the known percentage before working back to the original amount.
🔄 Rule 1: Find the percentage left
Subtract the percentage used, spent, or removed from 100%.
Example: A bottle is 30% empty. That means 100% - 30% = 70% of its water remains.
🧮 Rule 2: Divide by the remaining decimal
If the amount left is known, divide it by the percentage left as a decimal.
Example: A bottle still contains 280 ml, which is 70% of its full capacity. Work backwards: 280 ÷ 0.70 = 400 ml.
➕ Rule 3: Combine changes first
When several percentages of the original total are removed, add them before finding what remains.
Example: Hugo gives away 10% of his toy cars, then another 40% of the original number. He keeps 30 cars. Since 50% remains, he started with 30 ÷ 0.50 = 60 cars.
✅ Rule 4: Answer the exact question
Some questions ask for the original total. Others ask how much was spent or what percentage was lost.
Example: John donates 55% of his charity money and has £180 left. The £180 is 45% of the total, so he started with £400. The question asks what he donated: £220.
How to Solve Reverse Percentage Questions
One straightforward example, one multi-step example, and one classic mistake to avoid.
1. Recover the Original Total
Question: A water bottle is 30% empty and still contains 280 millilitres of water. What is the full capacity of the bottle?
Worked Method
Step 1: If the bottle is 30% empty, then 100% - 30% = 70% remains.
Step 2: Write 70% as 0.70. The full capacity is 280 ÷ 0.70 = 400 ml.
Tip: The known amount is often the percentage left, not the percentage removed.
2. Combine Percentages Before Working Backwards
Question: Hugo donates 10% of his toy cars, gives 40% of the original number to his cousin, and keeps the remaining 30 cars. How many toy cars did he have originally?
Worked Method
Step 1: Add the two percentages given away: 10% + 40% = 50%.
Step 2: The remaining percentage is 100% - 50% = 50%.
Step 3: If 50% is 30 cars, the original number is 30 ÷ 0.50 = 60 cars.
Tip: Check whether each percentage refers to the original total before adding them.
3. Do Not Stop at the Original Total
Question: John donated 55% of some charity money and still had £180 to donate later. How much money did he donate first?
Worked Method
Step 1: The percentage left is 100% - 55% = 45%.
Step 2: The original amount is £180 ÷ 0.45 = £400.
Step 3: John donated 55% of £400: £400 × 0.55 = £220.
The trap: £400 is a useful intermediate value, but it is not the answer requested.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Reverse Percentages pack contains 90 word problems across 3 printable test sets. Students practise finding original amounts, combining percentage changes, and checking what each question asks for.
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