There is no paradox.
We start out at
1 ounce of hummus1 dollar.
If in a year, the price of hummus is
1 ounce of hummus1.25 dollars, then we say that the price of hummus (in terms of dollars) has gone up by 25%.
If in a year, the price of hummus is
1 ounce of hummus0.80 dollars, then we say that the price of hummus (in terms of dollars) has gone down by 20%.
Now that is how we normally think about prices in the US because our medioum of exchange, standard of value, and legal tender is the dollar. We are thinking in terms of the dollar. It is, to use the technical term, the numeraire.
Now let's think about foreign exchange.
We start out at
1 euro1 dollar a year ago.
If the price of euros is
1 euro1.25 dollars, then we say that the value of euros (in terms of dollars) has gone up by 25% (just like the hummus example). But that means the value of a dollar in terms of euroes has gone down. How much?
Well, obviously,
[math]\dfrac{1 \text { euro}}{1.25 \text { dollar}} = \dfrac{0.8 \text { euros}{1 \text { dollar}}.[/math]
The value of the dollar has gone down by 20% in terms of euroes. It depends on our frame of reference whether euroes appreciated by 25% in terms of dollars or whether dollars depreciated by 20% in terms of euros. If you are an American who bought euros a year ago for dollars, you will enjoy your vacation in France. If you are French and bought dollars a year ago for euros, you will not be happy that you did not.
When we are talking about the price of money, we need to realize that we can choose either currency as the numeraire (the numerator), and that in general the reciprocal of a number equals itself only if the number is 1.
The guy said it was a brain teaser, not a paradox. He carefully started with a 1 to 1 ratio and chose a pair of numbers whose reciprocals equaled each other. If you play around with foreigh exchange, you quickly get used to playing with reciprocals and frames of reference. There is no esoteric anything going on. It is just that we Americans are not used to thinking about anything but dollars in the numerator of a price. It's a Brit laughing at the stupid colonists across the Atlantic.