Bag \(1\) contains \(4\) white balls and \(5\) black balls, and Bag \(2\) contains n white balls and \(3\) black balls. …

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 :

[JEE Main 2025, 29 Jan (Shift 2)]