For parallel reaction

When adding the rate constants of the two reactions, we need to use the formula for combining rate constants of two reactions in parallel, which is:

$\mathrm{k}={\mathrm{k}}_1+{\mathrm{k}}_2$

where ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are the rate constants of the individual reactions.

In this case, the half-lives of the two reactions are $12$ min and $3$ min, respectively. The rate constants of the two reactions can be calculated using the formula for half-life of a first-order reaction:

$\frac{1}{{\mathrm{t}}_{1/2}}=\frac{1}{12}+\frac{1}{3}=\frac{5}{12}$

Net ${\mathrm{t}}_{1/2}=\frac{12}{5}=2.4 \min \approx 2 \min$

Hence time taken for $50\%$ consumption of reactant will be close to $2 \min$.