Stations X and Y are 500 km apart. A train starts from X toward Y at 20 km/h. At the same time, another train starts from Y toward X at 30 km/h. At what distance from X will the two trains meet?

Introduction / Context:
Two trains start simultaneously from opposite ends of a straight 500 km track. We are asked for the meeting point measured from station X. This is a standard opposite-direction relative-speed problem.

Given Data / Assumptions:

• Total distance between X and Y = 500 km.
• Speed from X = 20 km/h.
• Speed from Y = 30 km/h.
• They start at the same time and move uniformly.

Concept / Approach:
When objects move toward each other, the effective closing (relative) speed is the sum of their speeds. Meeting time = total distance / (sum of speeds). Meeting distance from a given end equals that end's train speed * meeting time.

Step-by-Step Solution:
Relative speed = 20 + 30 = 50 km/h.Time to meet t = 500 / 50 = 10 h.Distance from X at meeting = 20 * 10 = 200 km.

Verification / Alternative check:
Distance from Y at meeting = 30 * 10 = 300 km. 200 + 300 = 500 km, matching the total separation.

Why Other Options Are Wrong:
30 km, 40 km, and 120 km do not satisfy the distance balance with the given speeds and simultaneous start.

Common Pitfalls:
Subtracting speeds (used for same-direction chasing), or forgetting to multiply the meeting time by the speed of the train from X to locate the meeting point.

Final Answer:
200 km