Hour hand will cover 360 degrees in 12 hours. Thus, 1 hour = 30 degrees.
In 2 hour 20 minutes i.e. in 2.33 hours it will cover 2.33*30 = 70 degrees.
Minute hand will cover 360 degrees in 1 hours. Thus, in 20 minutes it will cover 120 degrees.
Thus, the angle between the hour hand and the minute hand at 2 hour twenty minutes = 120-70 = 50 degrees.
Hence, option B is the correct answer.