The rate of a first order reaction is $0.06\text{ mol L}^{-1}\text{ s}^{-1}$ after 20 seconds and $0.03\text{ mol L}^{-1}\text{ s}^{-1}$ after 30 seconds from the start of the reaction. The half life period of this reaction is

$ 10\ \text{s} $

The correct answer is Option (3) → $ 10\ \text{s} $

The reaction is first-order (given)

Rate at $t_1=20s$ is $0.06\text{ mol L}^{-1}\text{ s}^{-1}$

Rate at $t_2=30s$ is $0.03\text{ mol L}^{-1}\text{ s}^{-1}$

In a first-order reaction, the rate is directly proportional to concentration:

Rate = k[A] (rate law expression)

If you observe values, Rate got exactly half between time of 30 secs and 20 secs. So, Half-life is 10 sec