📖 Reverse Percentage Word Problems

About Reverse Percentage Word Problems

Reverse percentage is the question that catches out pupils who are perfectly fluent going forwards. Told that a price is one hundred and twenty pounds after a twenty per cent increase, the instinctive move is to take twenty per cent off — which gives ninety-six, and is wrong, because the twenty per cent was of the original and not of the new figure. The correct move is to divide by the multiplier, and this worksheet exists to make that division automatic. Every problem states the changed value and asks for the one before it, so there is never any doubt about which figure is which. The answer key gives the divisor as well as the answer, making the method visible. Behind each question the problem is built forwards — an original amount, a multiplier, a result — and then presented backwards, which guarantees the original is exactly recoverable and never a recurring decimal. All the arithmetic is in whole pence. The levels move from simple increases, to decreases, to larger values, to less obvious percentages, and finally to two changes that must both be undone, in the right order. Six problems per page with ruled working space. Each level prints as a clean A4 sheet in black and white with its own separate answer key. It pairs with Percentage Multiplier Sim, the forward version of the same idea.

Common questions

Why can I not just subtract the percentage?

Because the percentage was of the original, not of the new figure. Taking 20% off £120 gives £96, but the original was £100.

Is the original always recoverable exactly?

Yes. Each problem is built forwards and presented backwards, so the original is never a recurring decimal.

Does the key show the method?

Yes — it gives the divisor as well as the answer.

What happens at the highest level?

Two changes must both be undone, in the right order.