Speed of Train A — which statements suffice? I. Train A crosses a 200 m long Train B running in the opposite direction in 20 s. II. The speed of Train B is 60 km/h. III. The length of Train A is twice the length of Train B.

Introduction / Context:
Data sufficiency problems ask which statements provide enough information to uniquely determine the answer. Here, we must decide which of I, II, and III are necessary to compute the speed of Train A when the trains cross each other in opposite directions.

Given Data / Assumptions:

• I: Crossing time of the two trains is 20 s; Train B's length is 200 m.
• II: Speed of Train B = 60 km/h.
• III: Length of Train A is twice that of Train B.
• Standard relation for opposite direction crossing: time = (LA + LB) / (vA + vB), with consistent SI units (m, m/s).

Concept / Approach:
Convert km/h to m/s as needed. Use the crossing-time formula to compute the relative speed (vA + vB) from total length (LA + LB), then isolate vA using vB from II. To get (LA + LB), we need both LA and LB; I gives LB = 200 m, but not LA. III links LA to LB so LA = 2 * LB = 400 m, hence total 600 m.

Step-by-Step Solution:

Verification / Alternative check:
Plug vA = 48 km/h (13.333... m/s) and vB = 60 km/h (16.666... m/s): relative speed 30 m/s; total length 600 m; time = 600 / 30 = 20 s, matching statement I.

Why Other Options Are Wrong:

• I and II only: Missing LA; can't compute total length to get relative speed.
• II and III only: Missing the 200 m from I; can't get absolute lengths.
• I and III only: Relative speed remains unknown without vB.

Common Pitfalls:
Using 60 km/h without converting to m/s; assuming LA is known from I alone; forgetting that crossing time depends on total length, not a single train's length.

Final Answer:
All, I II and III