Reverse Percentage

Reverse Percentage


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.


1. 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.

Answer: £11400

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

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

Answer: £186.62

Sale price = original price x multiplier

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

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


= £186.62 (2 dp)