Reverse Percentage

# Reverse Percentage

GCSE(F),

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.

## Examples

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.

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?

frac(text(sale))(text(multiplier)) = original
Multiplier = 1 - frac(25)(100) = 0.75 (reduction, so subtract)
frac(139.99)(0.75)