Potato Paradox

Paradox

I dug my potatoes out of the ground after a particularly wet season when my garden got badly waterlogged.

When I finally got them up, I found that of my $100 \, \mathrm {kg}$ of taties, they were $99 \%$ water. Very soggy potatoes.

So I set them in the (finally arrived) sun to dry for a bit.

When I looked at them next, they were now $98 \%$ water.

How heavy are my taters now?

$50 \, \mathrm {kg}$.

What, really?

Let $x \, \mathrm {kg}$ denote the dry stuff in the potato.

We have by hypothesis that $x$ forms $1 \%$ of the mass of the potatoes before we start drying them.

That is, $x = \dfrac 1 {100}$ of $100 \, \mathrm {kg}$:

$x = 1 \, \mathrm {kg}$

After drying them, $x$ is $2 \%$, or $\dfrac 1 {50}$, of the mass of the potatoes.

But still $x = 1 \, \mathrm {kg}$.

So the weight of the potatoes after drying them is $50 \, \mathrm {kg}$.

$\blacksquare$