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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What Do Reverse Percentage Questions Look Like?
Reverse percentage questions ask you to work backwards from a final amount, percentage change, or amount remaining to find the original total. You are given a quantity after an increase, decrease, or discount, and you need to determine the starting value before that change took place. Here is a worked example.
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.
Rules to Help You Solve Reverse Percentage Questions
These worksheets include finding an original amount from a known percentage, finding how much was spent or donated, and calculating the percentage lost when the original and remaining amounts are given. Using the approach from the example above, first identify which quantities are known and what the question asks you to find.
🔄 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.
If the original and remaining amounts are given, use:
Percentage lost = (original − remaining) ÷ original × 100.
Example: A tank originally holds 500 litres and has 450 litres left after a leak. The percentage lost is (500 − 450) ÷ 500 × 100 = 10%.
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.
Two More Worked Examples
Here are two additional problems showing how to combine percentages before calculating and how to avoid the common trap of stopping at an intermediate value.
Combine Percentages Before Working Backwards
Question: Hugo has a collection of toy cars. He donates 10% of the original number of 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.
Finding the Amount Removed
Question: John raised some money for charity. He donated 55% of it and still had £180.00 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.
