c
(c) The situation is shown in the fig.
Both the source (engine) and the observer (Person in the middle of the train) have the same speed, but their direction of motion is right angles to each other.
The component of velocity of observer towards source is $v\cos 45^\circ $ and that of source along the time joining the observer and source is also $v\cos 45^\circ $.
There is number relative motion between them, so there is no change in frequency heard. So frequency heard is $200 Hz.$
