How to find out the amount without VAT?
$$£\,3.325 + 20\,\% = £\,3.99$$
but, if I do $£3.99 – 20\% = £3.192$ instead of $£3.325$, how can I find out $£3.325$ out of $£3.99$?
[Math] Find the original value without VAT
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percentages
How to find out the amount without VAT?
$$£\,3.325 + 20\,\% = £\,3.99$$
but, if I do $£3.99 – 20\% = £3.192$ instead of $£3.325$, how can I find out $£3.325$ out of $£3.99$?
Best Answer
Assume you want to add a percentage $p\%$ to a given number $x$. What you have denoted by the expression "$x+p\%$" for the final price $y_1$ means the following: $$y_1=x + \frac{p}{100}\cdot x = x\cdot\left(1 + \frac{p}{100}\right)$$
On the same way, "$x-p\%$" gives a different price $y_1$: $$y_2=x - \frac{p}{100}\cdot x = x\cdot\left(1 - \frac{p}{100}\right)$$
Thus, in your particular case, you have to recover $x$ from $y_1$ and, hence, you have to divide that quantity by $1.20$. Note that this is not the same as what you did. You multipled by $0.8$:
£3.99 / 1.20 = £3.325£3.99 · 0.8 = £3.192