Question 4 - 2021 (25 Feb Shift 1)

A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform speed. At that point, angle of depression of the boat with the man’s eye is $30°$. After sailing for 20 seconds towards the base of the tower, the boat has reached a point B, where the angle of depression is $45°$. Then the time taken (in seconds) by the boat from B to reach the base of the tower is:

(1) $10(\sqrt{3} - 1)$ (2) $10\sqrt{3}$ (3) $10$ (4) $10(\sqrt{3} + 1)$