Processing math: 100%

The Potato Paradox

seen here

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