# The Potato Paradox
[seen here](https://www.reddit.com/r/math/comments/9h893j/potato_paradox/)

You have $100kg$ of potatoes, each containing $99\\%$ water.
 You leave them to dry until they each contain $98\\%$ water.
 You now have only $50kg$ of potatoes.
 

Proof:

Let $p$ be the weight of the potatoes
$$
p = 100kg
$$
and $w$ the water content
$$
w = \frac{99 \cdot 100kg}{100}
$$
We know $d$ the dry content is
$$
d = \frac{1 \cdot 100kg}{100}
$$
Thus the ratio between $d$ and $w$ is $1:99$ and $d + w = p$.

At $98\%$ water, the ratio becomes $2:98$ or $1:49$.
 Thus the new water content $w'$ is
$$
w' = \frac{49 \cdot 100kg}{100}
$$
and the new weight is
$$
p' = w' + d = 50kg
$$