Full Cup Tea and Coffee


Suppose we lay down two cups in front of you. One of the cups is filled with tea and the other one with coffee. Now we ask you to take a spoonful of tea and mix it with the coffee. At this moment, the coffee cup has a mixture of tea and coffee. You have to take that mixture (spoonful) and add it back to the tea.

Can you now tell if the cup of coffee has more tea or the cup tea has more coffee?

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  • 1 Answer(s)

    The amount is the same. Without going into formulas lets look on an endpoint where we mix the two cups together. The mixture will be half coffee and half tea and after returning to the original cup each cup will be the same (half tea and half coffee.

    Still not convinced? Suppose we take a half cup from tea and add it to the coffee cup. So the amount of tea in the mixture will be 0.5x(x+0.5x) = 1/3 so  the amount of coffee is 2/3. Now each half (from the 3 halves) has the same mixture. So now we take one of those halves and put it back to the original cup (of tea). We have a 1/2 cup of tea and another half cup which 2/3 of it is coffee, so in the whole cup the coffee will be only 1/3 just like the amount of tea on the other cup.

    Moshe Expert Answered on 7th December 2022.
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