Bunuel
I solved this question in less than 10 seconds, I was surprised to find out that it is 95% hard. I probably did something wrong and was lucky to get the correct answer. Please look at what I did and correct me, where I'm wrong.
Since the question stem indicates that the diagram is not drawn to scale, using the provided info, I drew a proper diagram with decent semi-circles.
Instead of using angle YXA as 105°, I turned it upside down and used angle ABY as 105°. Since we are only looking for the ratio of the regions, irrespective of which position the degree is coming from.
Thus,I had the upper shaded region to be 105°, and the lower region to be therefore (360-(180+105)) = 75°.
I went ahead to compute 105/75 = 7/5.
It might seem pretty long but it was pretty fast. Although it seems like a ludicrous luck!