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In a store window, there was a flat containing boxes of berries having a total weight of 100 kg. An analysis showed that the berries were 99% moisture, by weight. After two days in the sun, a second analysis showed that the moisture content of the berries was only 98%, by weight. What was the total weight of the berries after two days, in kg?

Did any of you get 50kg because I got something like 98kg and I'm totally wrong? :(

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  • $\begingroup$ It is 50 kg. How did you get 98? $\endgroup$ – Don Thousand Feb 6 at 2:09
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    $\begingroup$ This is sometimes known as the Potato Psradox. You have to think about the non-water part of the berries, which doesn't lose weight, and what it's $1\%$ or $2\%$ of. $\endgroup$ – timtfj Feb 6 at 2:12
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You have to think about the non-water content, not the water.

Initially, the berries are $1\%$ solids, and all the rest is water.

After drying out, they're $2\%$ solids, and all the rest is water.

The solids haven't changed weight. So if they've gone from being $1\%$ to $2\%$ of the total weight, the total weight must have halved.

The thing with this one, known as the Potato Paradox, is that it feels intuitively wrong even after carefully working it out and getting the right answer. Instinctively we feel the water has gone down to $\frac{98}{99}$ of what it was, but instinct turns out to be wrong.

I think it's because we're used to comparing percentages of some fixed total amount, while here the total amount is what changes.

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