The correct option is C.
Step-by-step explanation:
It is given that CD is the perpendicular bisector of both XY and ST, and CY=20.
In triangle XCD and YCD,
            (Common sides)
       (Definition of perpendicular bisector)
       (Definition of perpendicular bisector)
By SAS postulate of congruent triangles,
The corresponding parts of congruent triangle are congruent,
        (CPCTC)
        (CY=20)
The length of CX is 20 units. Therefore the correct option is C.