If we look at the above image, A is the previous position of the boat. Angle of elevation from this point to the top of the light house is 30 degrees.
After sailing for 50 m, Anil reaches point D from where angle of elevation is 45 degrees. C is the top of the light house.
Let BD = x
Now, we know tan 30 degrees = 1/ √3 = BC/AB
Tan 45 degrees = 1
=> BC = BD = x
Thus, 1/ √3 = BC/AB = BC / (AD+DB) = x / (50 + x)
Thus x (√3 -1) = 50 or x= 25(√3 +1) m
The answer is Option D.