Question

Coffee and Tea Volume Riddle (for fun)

Answer 1

There are two equally sized cups. The first cup has exactly 100 mL of coffee. The second cup has exactly 100 mL of tea. One spoon of coffee is taken from the coffee cup and mixed into the tea cup. Then, one spoon is taken from the tea cup and mixed back into the coffee cup.

Does the coffee cup have more tea in it or does the tea cup have more coffee in it?

Answer 2

(assume the spoons are equal in volume)

Answer 3

@Ultrilliam @Elsa213 @JoyLoveReynolds @theDeviliscoming I pick these 4 peeps to try *-* Can't back out

Answer 4

@sillybilly123 @sweetburger

Answer 5

Both are the same. o:

Answer 6

and I know the answer, as I had this exact riddle in a advanced class i had in elementary

Answer 7

I think
>.>
<.<

Answer 8

(every day they would have a riddle on the board to solve)

Answer 9

However I can't give the math to prove my answer here so oh well

Answer 10

Your intuition is correct, the volumes of coffee in the tea and tea in the coffee are equal. Here is my attempt at a mathematical proof:

Answer 11

At the beginning, let y = the amount of coffee/tea in the cups and let x = the volume

Answer 12

After the first spoon is taken from the coffee, we have:

cup A: y - x mL coffee
cup B: y mL tea and x mL coffee

Answer 13

When we take the second spoonful from cup B, the contents of the spoon are:

x/(x+y) mL coffee and x - x/(x+y) tea

Answer 14

Therefore, after the second spoon is put back into cup A:

cup A: x - x/(x+y) mL tea
cup B: the original spoonful of coffee added (x) minus the amount of coffee taken during the second spoonful x/(x+y)

giving us x - x/(x+y) mL of the opposite drink in each cup

Answer 15

@sillybilly123 @sweetburger can you check my proof?

Answer 16

@Nnesha

Answer 17

*** I meant to say x = the volume of the spoon

Answer 18

*-*

Answer 19

looks close but on rapid inspection i am not so sure. i have typed it out this way.

Start:
Coffee Cup: C:100 ml, T:0 ml

Tea Cup: C:0 ml, T:100 ml

Transfer x ml coffee to Tea Cup to get:

Coffee Cup: C:100-x ml, T:0 ml

Tea Cup: C:x ml, T:100 ml

Mixture in Tea Cup is now in ratio: C:T = \(\dfrac{x}{100 + x} : \dfrac{100}{100 + x}\)

So you transfer x ml back to Coffee Cup in these measures:

- Coffee: \(x \cdot \dfrac{x}{100 + x} \) ml

- Tea: \(x \cdot \dfrac{100}{100 + x}\) ml

Coffee in Tea Cup is: \(x - x \cdot \dfrac{x}{100 + x} \qquad \triangle\)

Tea in Coffee Cup is: \( x \cdot\dfrac{100}{100 + x}\qquad \square\)


But.....

\( \triangle = x - x \cdot \dfrac{x}{100 + x}= x \left( 1 - \dfrac{x}{100 + x}\right)

\(= x \left( \dfrac{100 + x - x}{100 + x}\right) = \square\) !!

So they are the same.

🤔

The mixing bit is the key