One. (20 points) There are three stocks $A$, $B$, and $C$, and the purchasing situation of 28 investors is as follows: Each investor has bought at least one of the stocks; Among those who did not buy stock $A$, the number of people who bought stock $B$ is twice the number of people who bought stock $C$; Among those who bought stock $A$, the number of people who only bought stock $A$ is one more than the number of people who bought stock $A$ and other stocks; Additionally, among those who only bought one stock, half did not buy stock $A$. What percentage of the 28 investors only bought stock $B$?
Let the number of people who only buy stock $A$, stock $B$, and stock $C$ be $x$, $y$, and $z$ respectively. Among those who do not buy stock $A$, the number of people who buy both stocks $B$ and $C$ is $m$. Among those who buy stock $A$, the number of people who buy at least one of stocks $B$ or $C$ is $n$ (as shown in Figure 8).
From the problem, we have
$$
\begin{array}{l}
x+n+y+m+z=28, \\
y+m=2(z+m) \Rightarrow m=y-2z, \\
n=x-1, \\
\frac{1}{2}(x+y+z)=x \Rightarrow x=y+z .
\end{array}
$$

Substituting equations (2), (3), and (4) into equation (1), we get
$$
z=29-4y \geqslant 0 \Rightarrow y \leqslant \frac{29}{4} \text{. }
$$

From equation (2), we get
$$
\begin{array}{l}
m=9y-58 \geqslant 0 \Rightarrow y \geqslant \frac{58}{9} . \\
\text{ Hence } \frac{58}{9} \leqslant y \leqslant \frac{29}{4} .
\end{array}
$$

Since $y$ is an integer, $y=7$.
Thus, $z=1$, $m=5$, $x=8$, and $n=7$.
Therefore, the proportion of 28 investors who only buy stock $B$ is $7 \div 28 \times 100 \% = 25 \%$.