50% of a reaction occurs in 100 second and 75% of the reaction occurs in 200 second, the order of this reaction is 1.

Let the initial reactant concentration is 1 M.

In the first 100 seconds, reactant concentration is reduced to $50\% \mathrm{or} 1\times \frac{50}{100}=0.5 \mathrm{M}.$

In the second 100 seconds (total 200 seconds from start), reactant concentration is reduced to $100-75=25\% \mathrm{or} 1\times \frac{25}{100} =0.25 \mathrm{M}.$.

Thus, we observe that after each 100 second period, the reactant concentration is reduced to one half. Hence, 100 seconds is the half-life period and is independent of reactant concentration. This is characteristic of the first-order reaction.

First-order reaction as the half-life is constant.