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 = [tex]\frac{2}{3} *90 = \frac{180}{3} =60[/tex]
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 = [tex]\frac{1}{3} *60 = 20[/tex]
Thus there are 20 runners remaining at the end.
