The Potato Puzzle

There are two methods of solving this problem.

Method 1: The explanation states that the non-water weight is 1 kilo (1% of 100 kilos). Once the potatoes have dehydrated, the question becomes "1 kilo is 2% of how many kilos?" (there was no change in the non-water weight, only the composition), and in order for the percentage to be twice as big, the weight must be half as heavy.

Method 2: The initial ratio of potato stuff to water is 1:99. If the water is reduced to 98%, the potato stuff accounts for 2% of the weight, meaning the ratio becomes 2:98, or 1:49. Since the potato stuff still weighs 1 kilo, the water must weigh 49 kilos totalling 50 kilos.

On the first day, the 100 kg potatoes is 99% by weight. This means that the dry potato material weighs 1 kg or its dry weight $w_{dry} = 1$ . Let the weight of the potatoes be $w$ the next day. Then we have:

$\begin{aligned} \frac {w-w_{dry}}w & = 0.98 \\ \frac {w-1}w & = 0.98 \\ w - 1 & = 0.98w \\ \implies 0.02 w & = 1 \\ w & = \boxed {50} \end{aligned}$