Two sprinters run the same race of $100$ m. One run at a speed of $10$ metres per second and the other run at $8$ metres per second. By what time will the first sprinter beat the other sprinter?

The correct option is C: $2.5$ sec

$\text{Speed}=\frac{\text{distance}}{\text{time}}$

$\therefore$ $\text{Time}=\frac{\text{distance}}{\text{speed}}$

Speed of the first sprinter $=10$ metres per second. ($m{s}^{-1}$)

Time taken by first sprinter
$=\frac{100m{s}^{-1}}{10s}=10$ second

Speed of the second sprinter $=8$ metres per second. ($m{s}^{-1}$).

Time taken by second sprinter

$=\frac{100m{s}^{-1}}{8s}=12.5$ second

Difference in time = 12.5 - 10 = 2.5 second

So, the correct option is option C: 2.5 second.