Why the concentration with respect to time equation of a first-order reaction does not depend on the stoichiometric coefficient of reactant?
The key point which you will study in advanced classes, is the concept of elementary reactions. When a given reaction is an elementary reaction, the stoichiometric coefficients become the power of the rate law or in better words, the reaction order corresponds to the stoichiometric coefficients.

Definition of elementary reaction: An elementary reaction is a chemical reaction in which one or more chemical species react directly to form products in a single reaction step and with a single transition state (more details on elementary reactions).

Rate of reactions are determined by experiments. We never write the rate law based on the balanced equation. Compare this with equilibrium constant where coefficients are important. Even $\ce{2 A -&gt; B}$ may be proceeding in several elementary steps. The observed rate may be the effect of several combined elementary reactions. 

In those kinetic problems like yours, the writer will tell you the order of the reaction. Don't proceed to write the rate law on the basis of balanced equation. 

Reaction rate and writing the rate law are two different things. For a reaction

$$\ce{a A + b B → p P + q Q}$$

Reaction is written as 

$$r = -\frac{1}{a}\frac{\mathrm d[\ce{A}]}{\mathrm dt} = -\frac{1}{b}\frac{\mathrm d[\ce{B}]}{\mathrm dt} = \frac{1}{p}\frac{\mathrm d[\ce{P}]}{\mathrm dt} = \frac{1}{q}\frac{\mathrm d[\ce{Q}]}{\mathrm dt}$$

but we cannot write the rate law i.e. you do not know what would be the order of the reaction in general.

The relation above only shows how the rate of disappearance of reactants and rate of appearance of products are related. It should not be used anywhere else. Your book answer is correct.