Distribution of Students by Grades

A school has a total of 600 students enrolled in various courses. The students are divided into two main categories based on their grades: students with grades A and students with grades B. Each student is categorized either as an A or a B student, and there are no students with grades below B.

The following information is provided:

1. The total number of A students is equal to twice the number of B students.

2. The ratio of A students to total students is 1:3.

How many students are in each category?