A **Reverse Percentage** is when the final amount and the percentage change are both known, but the original amount is unknown.

Instead of *multiplying* by the multiplier, *divide* by the multiplier.

The price of new cars are going up by 5%. If a new car is now being sold at £12000, what was the original price of the car? Give your answer to three significant figures.

New price = original price x multiplier

`frac(text(new price))(text(multiplier))` = original price

Multiplier = 1 + `frac(5)(100)` = 1.05

`frac(12000)(1.05)` = 11428.57

To three significant figures: £11400

Answer: £11400

The sale price of a jacket is £139.99. It is being offered at 25% off the original price. What was the original price?

Sale price = original price x multiplier

`frac(text(sale))(text(multiplier))` = original

Multiplier = 1 - `frac(25)(100)` = 0.75 (reduction, so subtract)

`frac(139.99)(0.75)`

= £186.62 (2 dp)

Answer: £186.62

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