The yellow coloring is a polar substance hence it dissolve in water. Blue dye is nonpolar hence it dissolves in less polar acetone.
In chemistry, there is a general rule that like dissolves like. A substance can only dissolve in another if there is some kind of intermolecular interaction between the substances.
The yellow food coloring is a polar substance hence it is able to dissolve in water which is a polar solvent. The blue dye is a nonpolar substance hence it dissolve in acetone which is a less polar solvent.
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