The correct answer is D. became desperate.
The old beggar ran amuck and began to throw stones at the passerby. This suggests that the beggar was in a state of desperation. He may have been feeling hopeless and without options, and he may have been lashing out in anger or frustration.
Option A, felt disgusted, is incorrect because there is no indication that the beggar was disgusted with anyone or anything. Option B, became annoyed, is incorrect because there is no indication that the beggar was annoyed with anyone or anything. Option C, ran about wildly, is incorrect because the beggar was not simply running about wildly; he was specifically running amuck and throwing stones at people.
Therefore, the correct answer is D. became desperate.