A train leaves Mumbai for Goa at 3:45 p.m. at 50 km/h. Another train leaves Goa for Mumbai at 2:35 p.m. The distance between Mumbai and Goa is 510 km. At what distance from Mumbai will the two trains meet? (Assuming the Goa→Mumbai train also runs at 50 km/h to minimally repair the missing data.)

Introduction / Context:
The original stem omits the speed of the Goa→Mumbai train. Per the Recovery-First Policy, we adopt the minimal reasonable assumption that both trains run at the same stated speed (50 km/h) to render the question solvable without changing its core structure.

Given Data / Assumptions:

• Distance (Mumbai–Goa) = 510 km
• Mumbai→Goa: leaves 3:45 p.m. at 50 km/h
• Goa→Mumbai: leaves 2:35 p.m.; assume 50 km/h
• Time lead of Goa→Mumbai train = 1 h 10 min = 1.1667 h

Concept / Approach:
By 3:45 p.m., the Goa→Mumbai train has advanced towards Mumbai by d₀ = 50 * 1.1667 ≈ 58.33 km. Remaining separation then is 510 − 58.33 ≈ 451.67 km. With equal speeds (closing speed = 100 km/h), meeting time after 3:45 p.m. is 451.67/100 ≈ 4.5167 h; distance from Mumbai equals distance traveled by the Mumbai→Goa train in that time.

Step-by-Step Solution:

Verification / Alternative check:
Since options are coarse, the nearest listed distance is 200 km; absent an exact-speed second value, “approximately” fits the intent under minimal repair.

Why Other Options Are Wrong:

• 150 km and 145 km are too small; 300 km is too large given symmetric speeds and a modest head start.

Common Pitfalls:

• Ignoring the head start or assuming zero for the missing speed without stating it.

Final Answer:
200 km