Let $A$ be the amount that Alicia has invested in the company. Let $\frac{x}{y}$ be the fraction of the company that she owns. So if $V$ is the total value of the company, then $A=\frac{x}{y}V$.
The old percentage profit was $P$. So the old profit was $\frac{P}{100}V$. Alicia got the fraction $\frac{x}{y}$ of this, so Alicia's old profit was $\frac{x}{y}\frac{P}{100}V=\frac{P}{100}\frac{x}{y}V=\frac{P}{100}A.$
Similarly, Alicia's new profit is $\frac{Q}{100}A,$ so the change in profit is $\frac{Q}{100}A-\frac{P}{100}A.$
This is equal to $I_a$. So $I_a=\frac{Q-P}{100}A,$ and therefore $A=\frac{100 I_a}{Q-P}.$
Note that the fraction $\frac{x}{y}$ turned out to be irrelevant, as of course did the fact that there are other shareholders.