There would be the same amount of water in the milk as milk in the water, the percentages would be dependant upon the amount of liquid in the glasses and the size of the spoons. example glass holds 60ml, the big spoon hold 30ml. You put 30ml of milk into the water so that the mixture is now 1/3 milk (60ml water 30ml milk), when you transfer back 30ml if liquid this will be 10ml milk and 20ml water, leaving 20ml milk in the 40ml water. So now you have 40ml milk with 20ml water and vice versa.
I chose these amounts because they are simple, please feel free to try with small spoons and/or bigger glasses.
Okay, I used the same methodology as Corran (except that you obviously can't fit 90ml liquid into a 60ml glass).
I used fractions throughout, so no absolute values, and worked out the concentration each of milk and water in each mixture at the end of the puzzle.
I first tried it with a spoon 1/3 the volume of the glass and each glass starting 2/3 full. You put half of the milk in the water, resulting in a mixture of 2/3 water, 1/3 milk. You take 1/3 of this mixture and put it back in the milk (bringing it back to its original volume), resulting in a mixture of 2/3 milk, 1/3 water. Suggests Corran was right.
Tried it with a spoon 1/4 volume of glass and glasses starting 3/4 full, ended up with 3/4 water, 1/4 milk in what was originally water, and 3/4 milk, 1/4 water in what was originally milk. So it doesn't actually matter what size glass or spoon you use, or what the ratio of sizes is, as long as you thoroughly mix the solutions and use the same size spoon for each transfer. You will end up with the same concentration of "impurity" in each solution.
Does this qualify as a logical answer from a female? (I could be completely wrong of course.... I'm not very good at these things.)
Yup, you are absolutely right; the logical deduction is that the amounts mirror; the mix makes no different so no matter what the mix will be the same.
This is one that a person either gets right at once or totally wrong...
"I buy a painting for $70, sell it for $80, buy it for $90 and then sell it
for $100. How much profit do I make?"
And despite how it looks it is not a maths problem!