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# Reverse Percentages

### Reverse Percentages

Reverse percentages allow us to work out the original quantity once we know the amount that it has changed by.

Sometimes we are told the percentage change, but need to work out the original quantity. This is a reverse percentage.

Consider a situation like this: you receive a pay rise of $5\%$. Your current salary is now $\pounds30600$. What was your salary before the raise?

Think about what this means mathematically

You are earning $105\%$ of your previous salary. Therefore, multiplying the original amount by $1.05$ equals $\pounds30600$. Let's call the original amount $x$

Rearrange to find the original amount

$x \times1.05=30600$. Therefore, $x=\dfrac{30600}{1.05}$

Find $x$

$x=\dfrac{30600}{1.05}=30000$

Awesome! 🙌

Your original salary was $\pounds30000$

A price increases by $30\%$. By what should you divide to find the original?

If the new quantity is less than the original, the decimal multiplying the original will be **less than** 1.

You see that a t-shirt is reduced by 15% to £17. How much was it originally?

Think about the relative percentage

We have $85\%$ of the original amount, which we will call $x$.

Rearrange to find the original amount

$x \times 0.85=17 \rightarrow x=\dfrac{17}{0.85}$

Use the equation to find the original amount

$\dfrac{17}{0.85}=20$

Great work! 💪

The t-shirt was originally worth $\pounds20$

A price decreases by $20\%$. By what should you divide to get to the original price?

If a price decreases by $33\%$ By what should you divide to get to the original price?