B taking 3 step forward than taking 1 step in backward direction .
-----------1 sec----------> -----------2 sec----------> | -----------3 sec------------>
| <----------4 sec-------------
So resultant speed of B = 2 step / 4 second = 1/2 step per second
when escalator is not moving :
so in 116 seconds it will move 116*(1/2) = 58 steps forward
B reach at top in 118 seconds so , in next two second B will move 2 step forward .
so in 118 seconds B will move = 58+2 =60 steps
when escalator is moving :
Let speed of escaltor is X steps/ second .
now speed of B with respect to escalator = (1/2+X) steps/second
now B is reaching at the top in 40 seconds .
so 60 / (1/2+X) =40
X=(60/40)-(1/2)=1 steps /second
So option (A) is correct .