A train covers a certain distance in 50 minutes when it runs at an average speed of 48 km/h. At what speed (in km/h) must the train run so that the journey time is reduced to 40 minutes for the same distance?

Introduction / Context:
This question is a standard application of the distance, speed, and time relationship. The train first travels a certain distance at a known speed, and then we are asked to find a new speed that allows the same distance to be covered in less time. Problems of this type are common in aptitude tests for competitive exams.

Given Data / Assumptions:

- Initial average speed of the train = 48 km/h.
- Time taken at this speed = 50 minutes.
- New required time for the same distance = 40 minutes.
- Distance of the journey remains the same in both cases.
- Motion is along a straight track with constant speeds in each case.

Concept / Approach:
We first compute the distance covered using the initial speed and time. Then we use that fixed distance and the new travel time to determine the required new speed. The fundamental formula remains distance = speed * time. The main care needed is to keep all times in hours when using speeds in km/h.

Step-by-Step Solution:
Convert 50 minutes to hours: 50 / 60 = 5 / 6 hours. Distance of the journey = speed * time. Distance = 48 * (5 / 6) = 48 * 5 / 6 = 40 km. Now the same 40 km must be covered in 40 minutes. Convert 40 minutes to hours: 40 / 60 = 2 / 3 hours. Required new speed = distance / time = 40 / (2 / 3). Compute this: 40 * 3 / 2 = 60 km/h.

Verification / Alternative check:
At the original speed of 48 km/h, a 40 km journey would take 40 / 48 hours, which is 5 / 6 hours, equal to 50 minutes. At the new speed of 60 km/h, the time is 40 / 60 hours, equal to 2 / 3 hours, which is 40 minutes. This matches exactly the times mentioned in the problem, so our answer is consistent.

Why Other Options Are Wrong:
50 km/h: This would give a time of 40 / 50 hours = 0.8 hours, that is 48 minutes, which is still too long.
65 km/h and 70 km/h: These speeds would make the train arrive even earlier than 40 minutes, not exactly in 40 minutes, so they do not satisfy the given condition.

Common Pitfalls:
A common error is to attempt to scale the speed directly by the ratio of the times without carefully computing the distance first. Another frequent mistake is forgetting to convert minutes into hours before applying the formula, which leads to incorrect numbers. Always keep time units consistent with speed units during calculations.

Final Answer:
The train must run at an average speed of 60 km/h to reduce the journey time to 40 minutes.