Reverse Percentage Question Generator

A price is 480 after a 20% rise. Almost everybody's first answer is 384, because taking 20% off 480 feels like undoing the rise. It is not: the 20% was of the smaller number, and the answer is 400. This page sets that question over and over, always with a whole-number answer, and shows in the working why the division rather than the subtraction is the one that gets there.

How many questions

Between 1 and 30. Ten fills a page.

Level

Seed (optional)

A word reproduces the same sheet, so a whole class can be given the identical set.

Gentle uses 10%, 20%, 25% and 50%. Standard widens the set; stretch adds awkward percentages and rises above 100%.

Paper size

Print size

Margin

Millimetres of blank edge, 5 to 40.

Turn the paper sideways

Room to answer in

How to print this, or save it as a PDF

There is no PDF to download, and there does not need to be. Open the print command in your browser and choose “Save as PDF” as the destination. The page addresses and dates a browser normally prints across the top and bottom are already kept off.
Set the scale to 100%, not “fit to page”. This sheet is already the exact size of the paper you chose, so anything that resizes it makes every measurement on it wrong.
Leave the paper size in the dialog set to the same one you chose here.

Your questions will appear here.

What this generator does

Gives the value after a stated rise or fall and asks for the value before it — the question that the ordinary percentage sheet cannot ask, because it runs the calculation the other way. The working states the multiplier explicitly, which is the idea that makes every one of these questions the same question, and then checks itself forwards by applying the rise or fall to the answer and arriving back at the figure in the question.

How to use this tool

Choose how many questions you want and how awkward the percentages should be.
Press make questions, and work through the sheet.
Show the answers to mark it, or show the working to see the multiplier and the check done forwards.
Enter a seed word to rebuild exactly the same sheet later.

Understanding the controls

How many questions: One to thirty. Ten is plenty: this is one method applied repeatedly, and the value of the sheet is in noticing that it is always the same method.
Level: Gentle uses 10%, 20%, 25% and 50%, where the multiplier is easy to see. Standard widens the set. Stretch adds awkward percentages and rises above 100%, where the multiplier is more than two and the original is less than half of what is shown.
Seed: A word rebuilds the identical sheet, so two people can be set the same questions, or the same sheet reissued later as a retest.
Show the answers / show the working: The working names the multiplier, does the division, and then runs the change forwards on the answer to land back on the figure in the question — which is the check a reader should be doing themselves.

Common use cases

Reverse percentage practice at home or school
Working out a price before VAT or before a discount
Finding a starting figure from a percentage growth or drop
Self-testing before a maths exam, where this is a standard question

How this generator works

The questions are built in the only order that keeps the answer exact. The original amount and the percentage are chosen first and the after value is worked out from them, so the number a reader is asked to recover is always whole. Drawing the after value first and dividing would give originals like 483.333 and turn a reverse-percentage exercise into a rounding one. The check applies the stated rise or fall to the printed answer and requires it to land on the printed figure exactly, cross-multiplied so no step of the verification divides and nothing anywhere is rounded.

Randomness and fairness

The percentage is drawn first and the original is then drawn as a multiple of whatever makes the change come out whole, so the two are not independent — that constraint is what keeps every answer a whole number. Rises and falls are drawn evenly. Percentages of 100% or more are only ever offered as rises, because there is no way back from a fall of everything. A seed brings the same set of questions back, which is there for reproducibility, not cryptographic strength.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

Every original amount is a whole number, which is chosen for practice and unlike most real prices, where the answer to a reverse VAT calculation rarely comes out neatly.
Only one change is applied. Questions with a rise followed by a fall, where the two do not cancel, are a further step and are not set here.
A fall is never 100% or more, because there would be no original to recover from a value of nothing.
Seeded sheets repeat exactly, which makes the seeded path reproducible rather than unpredictable.

Common mistakes

Taking the percentage back off the figure you were given: Taking 20% off 480 gives 384, and adding 20% to 384 gives 460.8, not 480. The 20% was a share of the original, which is the number you do not yet know.
Dividing by the percentage instead of by the multiplier: After a 20% rise the new figure is 120% of the old one, so divide by 120 and multiply by 100 — not by 20.
Not checking forwards: Apply the stated rise or fall to your answer. If it does not land exactly on the number in the question, the answer is wrong, and this takes ten seconds.

Privacy and your data

The sheet is built inside your browser. Your level and seed are never uploaded, never stored and never sent to a server.