TITLE: Milk and Tea problem
QUESTION [6 upvotes]: There are two cups on a table. One is filled with tea, the other with milk. If we take a spoon of tea from the first cup and place that into the cup with milk and stir and then do the same but vice versa. Which was there more of in the end? Tea in the cup of milk or milk in the cup of tea?

REPLY [2 votes]: I think also the two cups may have different sizes and still, the amount of tea in the milk cup is the same as the amount of milk in the cup of tea. Consider the following:
The volume of the spoon is $V$, the amount of the tea transferred from the cup of tea into the cup of milk is $T_1$ (first spoon). So $$V=T_1$$Then you transfer a mixture of tea and milk from the cup of the mixture to the cup of tea (second spoon) where: $$V=T_2+M$$ Where $T_2$ and $M$ are the amount of tea and milk in the second spoon respectively. In the end, you will have $$(T_2+M)=T_1=V$$ So:

The amount of milk in the cup of tea is $M$
The amount of tea in the second cup is $T_1-T2$ (the amount of tea removed from the cup of tea) which equals to $M$

Please correct me if I am wrong.