Reverse Percentages (No Calculator) — KS3 Maths

A reverse percentage gives you the amount after a change and asks for the amount before. The key move is realising the number in front of you isn't 100% of anything — after 20% off, £160 is 80% of the original. Name that percentage, step down to 1%, and step back up to 100%.

What percentage are you actually holding?

This is the whole idea, and it's the step people skip. The amount you're given is a percentage of the original, and which percentage depends on what happened to it:

Once you've named it, one step down to 1% and one step up to 100% gets you back to the original.

Worked example

20% off → £160. What was the original?

Twenty percent came off, so £160 is only $80\%$ of the original. Divide by 80 to find $1\%$, then times by 100:

$1\% = 160 \div 80 = £2 \qquad 100\% = 2 \times 100 = £200$

The original price was £200.

Worked example

10% rise → £330. What was it before?

A $10\%$ rise means £330 is $110\%$ of the original:

$1\% = 330 \div 110 = £3 \qquad 100\% = 3 \times 100 = £300$

The original was £300.

Worked example

25% off → £300. Find the original.

Twenty-five percent off leaves $75\%$, so £300 is $75\%$ of the original:

$1\% = 300 \div 75 = £4 \qquad 100\% = 4 \times 100 = £400$

The original was £400.

Where you'll use this next

• Sale prices and VAT — working out a pre-VAT price, or an original price from a sale ticket.
• Percentage increase and decrease is the forward version; check a reverse answer by running it forwards.
• Index numbers and growth in later work use the same before-and-after reasoning.

Practice questions

Decide what percentage you've been given, divide to find 1%, then times by 100. Then click to check.