In a classroom containing only fifth- and sixth-graders,

5th grades are seated in 1/2 of the total desk.
6th grades are seated in 2/3 of the remaining desk.
i.e 6th graders = 2/3 of 1/2 = 2/3 * 1/2 = 1/3
Note: This is because if 5th grades are already using half of the desks available, that means that 6th grades are using only two-third of the remaining half/
Therefore, let the total number of desks = x
Hence, 5th grades = 1/2 * x = x/2
6th grades = 1/3 * x = x/3
Total number of desks in use = x/2 + x/3
$$=\frac{3x+2x}{6}=\frac{5}{6}\left(x\right)$$
The fraction of desk in use for 6th grades =
$$=\frac{6th\ grades}{desk\ in\ use}=\frac{\frac{1}{3}x}{\frac{5}{6}x}=\frac{1}{3}x\cdot\frac{6}{5}x$$
$$=\frac{2}{5}x^2$$
No matter what thevalue of x might be, 6th grades will always use 2/5 of the total number of disks.

Answer = option D