I always exaggerate everything I say by 25%. By how much do I truly exaggerate?

Question

'I always exaggerate everything I say by 25%. By how much do I truly exaggerate?'

Hi, I asked myself this question and it is starting to give me a headache. Does anyone have a correct solution? Thanks

Answer 1

$20.7\%$ approximately.

If you exaggerate by $x\%$ then you are multiplying by $1 + \frac{x}{100}$.

We know that $x \times (1 + \frac{x}{100}) = 25$.

Solving for $x$ using the quadartic formula leads to the correct result.

Nice question. :)

Answer 2

Let $x$ be the fraction you exaggerate everything by.

Then $25\%$ is equal to $x$ exaggerated by $x$, so $x(1+x) = 25\%$.

Solving this quadratic equation yields $x = \frac{\pm\sqrt{2} - 1}{2}$.

So either you exaggerate everything by $20.71067811865\%$, or you exaggerate everything by $-120.71067811865\%$.