Abdul can go from his home to his favourite basketball ground by taking any of the two roads represented by $$y - x = 10$$ and $$2x + 2y = 15$$. The ground is located at a distance of 200 units from each of the roads. What is the possible location of the basketball ground?

Since the question asks for a possible location of the ground, the most efficient way to solve such questions is to go by the options.

Option A:

Distance of point $$\left(-1.25+200\sqrt{2},\ 8.75\right)$$ from lines y-x=10 and x+y=15/2

Distance from y-x=10 is $$\frac{\left|1.25-200\sqrt{2}+8.75-10\right|}{\sqrt{\ 1}+\sqrt{\ 1}}=200$$

Distance from x+y=15/2 is $$\frac{\left|-1.25+200\sqrt{2}+8.75-7.5\right|}{\sqrt{\ 1}+\sqrt{\ 1}}=200$$

Since, in both cases, we are getting a distance equal to 200 units(equidistant from both roads), this is the correct option.

Thus, the correct option is A.