### Brain Teasers

# Anniversary

A French couple celebrates their 50th anniversary with a trip to Florida. One night they buy a bottle of wine that, even by French standards, is premium. They buy it with 130 Euros, and the exchange rate that day is 1.35 dollars per Euro. The restaurant charges a 3 percentage-point premium to exchange currencies. The wine was priced at $171.22 American, and the couple got five American coins back as change. Which five coins did they get?

### Hint

There are three types of coins.### Answer

They got one quarter, one dime, and three pennies. With a 1.35 exchange rate, after the three percentage-point premium they get 1.32 dollars per Euro. Paying 130 Euros*1.32 is $171.60 American dollars. The price is $171.22, for a difference of 38 cents. The only way to give that change with five coins is one quarter, one dime, and three pennies.Hide Hint Show Hint Hide Answer Show Answer

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## Comments

If the premium is 3 percentage points isntin it then 3% of 1.35 = 0.0405, making the effective rate 1.3095 instead of 1.32?

You're thinking percent. Percent and percentage points are measured differently, and I worded it as percentage points to avoid ambiguity. Percentage is a ratio of numbers, and percentage points are the absolute differences between numbers. An example from Wikipedia is:

Consider the following hypothetical example: in 1980, 40 percent of the population smoked, and in 1990 only 30 percent smoked. We can thus say that from 1980 to 1990, the incidence of smoking decreased by 10 percentage points even though smoking did not decrease by 10 percent (actually it decreased by 25 percent, assuming the same total population in both years) â€” percentages indicate ratios, not differences.

Consider the following hypothetical example: in 1980, 40 percent of the population smoked, and in 1990 only 30 percent smoked. We can thus say that from 1980 to 1990, the incidence of smoking decreased by 10 percentage points even though smoking did not decrease by 10 percent (actually it decreased by 25 percent, assuming the same total population in both years) â€” percentages indicate ratios, not differences.

I got it after peeking at the comments (but before peeking at the answer) and so gave you high marks for a good riddle.

But I must say, the percentage point technique for exchange premiums becomes very flawed if the currencies are not close in value. If I paid at that restaurant with Japanese Yen, valued today at 0.01313 Yen to the USD, the restaurant would have to take all my money, keep the wine, then slap me in the head and take my watch to make it come out even.

But I must say, the percentage point technique for exchange premiums becomes very flawed if the currencies are not close in value. If I paid at that restaurant with Japanese Yen, valued today at 0.01313 Yen to the USD, the restaurant would have to take all my money, keep the wine, then slap me in the head and take my watch to make it come out even.

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