Train A crosses a pole in 25 s. Train B crosses the same pole in 1 min 15 s. The length of Train A is half the length of Train B. Find the ratio of their speeds (A : B).

Introduction / Context:
Crossing a pole gives time = length/speed. With a known length relation (L_A = 0.5 L_B), we can form the ratio of speeds directly from times and lengths.

Given Data / Assumptions:

• T_A = 25 s, T_B = 75 s
• L_A = (1/2) L_B
• v_A = L_A / T_A, v_B = L_B / T_B

Concept / Approach:
Compute v_A : v_B = (L_A/T_A) : (L_B/T_B) = (L_A/L_B) * (T_B/T_A) = (1/2) * (75/25).

Step-by-Step Solution:

Verification / Alternative check:
Let L_B = 2 units ⇒ L_A = 1. Then v_A = 1/25, v_B = 2/75 ⇒ ratio (1/25):(2/75) = 3:2 ✔

Why Other Options Are Wrong:

• 3:4 and 4:3 invert or misapply the length/time relation.
• “Couldn’t be determined” is incorrect; data suffices.

Common Pitfalls:

• Forgetting length is proportional to speed times time.

Final Answer:
3 : 2