AMC 8 1991 Problem 17

An auditorium with $20$ rows of seats has $10$ seats in the first row. Each successive row has one more seat than the previous row. If students taking an exam are permitted to sit in any row, but not next to another student in that row, then the maximum number of students that can be seated for an exam is $\text{(A)}\ 150 \text{(B)}\ 180 \text{(C)}\ 200 \text{(D)}\ 400 \text{(E)}\ 460$