Mathematics Question from JEE Main 2025 · 29 January, Shift 2

Bag $1$ contains $4$ white balls and $5$ black balls, and Bag $2$ contains $n$ white balls and $3$ black balls. One ball is drawn randomly from Bag $1$ and transferred to Bag $2$. A ball is then drawn randomly from Bag $2$. If the probability that the ball drawn is white is $\frac{29}{45}$, then $n$ is equal to: