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 $30°$ (Ignore man's height). After sailing for $20$ seconds, towards the base of the tower (which is at the level of water), 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 :

• A

  $10$
• B

  $10(\sqrt{3}-1)$
• C

  $10\sqrt{3}$
• Correct answer
  D

  $10(\sqrt{3}+1)$

Hence, the correct answer is option: 'D'.