How to calculate concentration from reaction quotient and initial concentration?
You have everything you need.

$$\ce{A -&gt; B}$$

From the initial condition, stoichiometry and the conservation of mass, always:

$$\ce{[A] + [B]=1}$$

At time $t$:

$$\ce{\frac{[B]}{[A]}=1\to [B]=[A]}$$

Substitute into the first equation:

$$\ce{\to [A] + [A]=1\to 2\times [A]=1\to [A]=\frac12=[B]}$$

For a more general case:

$$\ce{[A] + [B]=n}$$

At time $t$:

$$\ce{\frac{[B]}{[A]}=Q\to [B]=Q\times [A]}$$

Substituting as above, we get:

$$\ce{[A]=\frac{n}{1+Q}}$$

$$\ce{[B]=\frac{n\times Q}{1+Q}}$$