C

Step 1: Let the velocity of the raindrops be \( v_r \) and the velocity of the man be \( v_m = 25 \, \text{m/s} \).
Step 2: When stationary, the rain strikes the man at an angle of \( 60^{\circ} \). This can be resolved into components:
\( v_{ry} = v_r \sin(60^{\circ}) \) and \( v_{rx} = v_r \cos(60^{\circ}) \).
Step 3: As the man moves, the effective angle of rain changes to \( 30^{\circ} \). At this angle, using relative motion,
\( v_{ry} = v_m + v_r \sin(30^{\circ}) \) and \( v_{rx} = v_r \cos(30^{\circ}) \).
Step 4: Setting the equations for vertical components:
\( v_r \sin(60^{\circ}) = 25 + v_r \sin(30^{\circ}) \)
Step 5: Setting up the equation for horizontal components:
\( v_r \cos(60^{\circ}) = v_r \cos(30^{\circ}) \)
Step 6: Now solving both equations gives simultaneous equations for \( v_r \).
Step 7: Solving results in \( v_r = 25 \sqrt{3} \, \text{m/s} \).
Therefore, option C is correct.