A man on the top of a vertical towers observes a car moving at a uniform speed coming directly towards it. if it takes 12 minute for the angle of depression to change from 30° to 45°, how soon after this will the car reach the tower?

Let us draw a figure below from given question.
Let AB = h meter be the height of the tower B and C are two points such that ∠ACB = 30° ∠ADB = 45° and CD = x meter (say)
From right triangle ABD,
tan 45° = h/BD
∴ BD = h meter;
Again from right triangle ABC
tan 30° = h/(h + x )
⇒ h + x = √3 h
∴ x = (1.73 - 1)h = 0.73h
Now, 0.73h meter covered in 12 min
Hence, h meter covered in 12/0.73 = 1200/73 min = 16 min 23 sec .