kinetics - Is half life for first order is depend on the stochiometric coefficient of reactant or product?

I took k=6.93x10^(-2) as given in ques and use the half life formula for 1st order kinetics and solve and finally get 10 min as a ans but right ans is 5 min and i m not able to get that..... Plse tell where i m doing mistake??

Answer

If the reaction has the form $aA \rightarrow B + C$ then the rate at which B and C are produced is $1/a$ of the rate at which A disappears, thus

$$-\frac{1}{a}\frac{dA}{dt}= \frac{dB}{dt}= \frac{dC}{dt}=kA$$

On this basis the half-life should be $5$ minutes in your question.