A molecule undergoes two independent first order reactions whose...

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:

$k = {k}_{1} + {k}_{2}$

where ${k}_{1}$ and ${k}_{2}$ 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:

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

Net ${t}_{1/2} = \dfrac{12}{5} = 2 . 4min \approx 2min$

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