There were 90 runners to start a race.
If 1/3 dropped out, that means only 2/3 of them are left, so we have:
Number remaining after the first round of dropout =

If 2/3 dropped out in the second half, only 1/3 of them are left, so we have
Number remaining after the second round of dropout =

Thus there are 20 runners remaining at the end.