Suppose you take 2 mL of boiling A.
X = 2 mL x 200 mg/mL = 400 mg so all of X will dissolve.
Y = 2 mL x 200 mg/mL = 400 mg so all of Y will dissolve.
Now cool the solution to room temperature. How much X and Y will recrystallize?
2 mL x 20 mg/mL = 40 mg X will stay in solution; 400 - 40 = 360 mg X will crystallize.
2 mL x 20 mg/mL = 40 mg Y will stay in solution; you had only 30 so none will crystallize.
I'm guessing that 2mL of boiling A came from (400mg)(1mL/200mg)= 2mL
So we don't have worry about the Y at boiling A? which will be 0.15mL if we do the calculation.
You add enough boiling A to dissolve all of X (of course it will dissolver all of Y, too). Using 0.15 mL of boiling A will dissolve all of Y and some of X. In fact I suppose you could get pure X this way, too, although it isn't the usual way we think of recrystallization.
200 mg/mL x 0.15 mL = 30 mg X will dissolve leaving 400-30 = 370 mg X behind, BUT
1. 0.15 mL is a small volume to be working with, and you would have trouble controlling the volume and losing volume as it sticks to the walls of the vessel,
2. I would want to add just a little more than 0.15 because this JUST barely gets all of Y in solution.
3. I doubt this is the way your prof expects you to answer.
I was also thinking so we can't add the two volume of A together? So like for X in boiling A there is 2mL and in Y there is 0.15ml. So all together solvent A would be 2.15mL.
all of Y would still be gone but for X instead of 360mg i would get 357mg
In general, we assume that we need only one volume. In this case, however, an extra 0.15 mL couldn't hurt anything. As you point, however, it affects the yield.