Step 1 :Let's denote the number of students who own an automobile as \(automobile_owners = 91\)
Step 2 :Let's denote the number of students who own a motorcycle as \(motorcycle_owners = 125\)
Step 3 :Let's denote the number of students who own both an automobile and a motorcycle as \(both_owners = 27\)
Step 4 :Let's denote the total number of students as \(total_students = 500\)
Step 5 :The number of students who own either an automobile or a motorcycle can be calculated by adding the number of students who own an automobile and the number of students who own a motorcycle, and subtracting the number of students who own both to avoid double counting. So, \(either_owners = automobile_owners + motorcycle_owners - both_owners = 189\)
Step 6 :The percentage of students who own either an automobile or a motorcycle can be calculated by dividing the number of students who own either an automobile or a motorcycle by the total number of students and multiplying by 100. So, \(percentage = \frac{either_owners}{total_students} \times 100 = 37.8\)
Step 7 :Final Answer: The percentage of students who own either an automobile or a motorcycle is \(\boxed{37.8\%}\)