Choose a sign convention
Take north as positive and south as negative.

Convert speeds into SI units $72\ \text{km/h} = 72\times \frac{5}{18} = 20\ \text{m/s}$ $108\ \text{km/h} = 108\times \frac{5}{18} = 30\ \text{m/s}$

Write velocities with sign

• Train A is moving north: $v_A = +20\ \text{m/s}$
• Train B is moving south: $v_B = -30\ \text{m/s}$

Velocity of train B with respect to A Relative velocity formula: $v_{B/A} = v_B - v_A$ $v_{B/A} = (-30) - (20) = -50\ \text{m/s}$

Velocity of ground with respect to B Ground is at rest in earth frame: $v_G = 0$ So, $v_{G/B} = v_G - v_B = 0 - (-30) = +30\ \text{m/s}$

Match with options The pair is: $(-50,\ 30)$ which corresponds to Option B.

Comparison with stored answer Stored correct answer is B, which matches our result.