Potato paradox

[Gavran]

100 kg of potatoes consists of 99% water. After some water evaporates, the potatoes consist of 98% water. What is the new weight of the potatoes? The answer is 50 kg.

The explanation is simple. 100 kg of potatoes consists of 99% water and 1% dry matter, so the weight of the dry matter is 1 kg. After some water evaporates, the potatoes consist of 98% water and 2% dry matter. The weight of the dry matter is still 1 kg, so 2% of the potatoes equals 1 kg. This means that 100% of the potatoes equals 50 kg.

Some people think the problem is not paradoxical and the answer is intuitive, but in my opinion, there is a paradox because a small 1% decrease in water content (from 99% to 98%) causes a large 50% decrease in the total weight of the potatoes.

 

[anuttarasammyak]

Salt matter condense up from 1% to 2% (doubles) by more than 50% water evaporation seems to be reasonable.

 

[Hill]

It seems paradoxical when one erroneously translates the "1% decrease in water content" as "1% of water evaporates."
If 100 kg potatoes consisted of 100% of water, it would stay 100% regardless of evaporation.

 

[PeroK]

Some people think the problem is not paradoxical and the answer is intuitive, but in my opinion, there is a paradox because a small 1% decrease in water content (from 99% to 98%) causes a large 50% decrease in the total weight of the potatoes.

It's only paradoxical if you insist on manipulating numbers without thining about what the numbers mean.

There was a viral problem in a Chinese exam that exploited this.

 

[Hill]

The guy in the video also makes logical mistakes, it seems. For example,

I doubt that the problem in China and in France has been asked in English. In this case, what does "in ALMOST EXACTLY the same wording" mean?
Both wordings are translations, not how the problem has been asked.