A bus travelled from station A to station E. There were 45 passengers on the bus when it left station A. At station B, some passengers boarded the bus but no passenger alighted from it. At station C, half of the passengers in the bus alighted and 20 passengers boarded it. Finally at station D, another half of the passengers in the bus alighted and 30 passengers boarded it. There were 80 passengers on the bus as it left station D for station E. How many passengers boarded the bus at station B?
At station D, another half of the passengers in the bus alighted, thus there were 80-30 = <<80-30=50>>50 passengers on the bus after half had alighted.
Since half of the passengers alighted, the number of passengers on the bus after 20 passengers boarded at station c was 50*2 = <<50*2=100>>100
There were 100-20 = <<100-20=80>>80 passengers on the bus before 20 more boarded.
At station C, half of the passengers in the bus alighted, meaning there were 80*2 = <<80*2=160>>160 passengers before half alighted.
Since there were 45 passengers on the bus when it left station A, the number of passengers that boarded the bus at station B is 160-45 = <<160-45=115>>115 passengers at station B. Answer: \boxed{115}.