Train A, travelling at 42 kmph, overtook train B, traveling in the same direction, in 20 seconds. If train B had been traveling at twice its speed, then train A would have taken 45 seconds to overtake it. Find the length of train B, given that it is half the length of train A.

Let L_A, L_B be lengths, S_A, S_B be speeds. S_A = 42 kmph = 35/3 m/s. Case 1: (L_A + L_B) / (S_A - S_B) = 20. Case 2: (L_A + L_B) / (S_A - 2S_B) = 45. Given L_B = L_A/2. From equations: (3L/2) / (35/3 - S_B) = 20 and (3L/2) / (35/3 - 2S_B) = 45. Solving gives L_B = 50m, S_B = 14 m/s, L_A = 100m. Option A (90.5) is incorrect. Option C (116.6) doesn't satisfy the conditions.