A train traveling at a speed of 90 km/hr crosses a man standing on a platform in 8 seconds. What is the time taken by the train to cross the platform of length 250 km?

Appeared in: AIIMS CRE SNO - 2023

Explanation

First, convert the train's speed from km/hr to m/s by multiplying by 5/18. This gives a speed of 25 m/s.
Next, calculate the length of the train. Since it crosses a man (a point object) in 8 seconds, its length is Speed × Time, which is 25 m/s × 8 s = 200 meters.
To cross the platform, the train must cover its own length plus the platform's length. The total distance is 200 m + 250 m = 450 meters.
Finally, the time taken is the total distance divided by the speed: 450 m / 25 m/s = 18 seconds.

Option A: This answer is incorrect. It might result from a miscalculation of the total distance or speed. For instance, if the total distance was incorrectly calculated as 600m, the time would be 600m / 25m/s = 24s.
Option C: This answer is incorrect. A time of 12 seconds would imply a total distance of 300 meters (12s * 25m/s). This could happen if the train's length was miscalculated.
Option D: This answer is incorrect. It is exactly double the correct answer. This could arise from an error like doubling the total distance (900m) or incorrectly applying the formulas.

Visual 1: Infographic: A visual diagram showing the two scenarios. First, the train of length 'L' crossing a pole, where the distance covered is 'L'. Second, the same train crossing a platform of length 'P', where the total distance covered is 'L + P'.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Problems on Trains (Quantitative Aptitude) as background academic context rather than a clinical decision trigger.
This question tests quantitative aptitude, which is a non-nursing subject but a critical component of the general intelligence and reasoning sections of many nursing competitive examinations.
Strong analytical and problem-solving skills are essential for nurses to interpret data, calculate dosages, and manage time-sensitive tasks effectively. Practicing such questions enhances these cognitive abilities.
What if the train was crossing another moving train instead of a stationary platform? The concept of relative speed would need to be applied, where speeds are added if moving in opposite directions and subtracted if moving in the same direction.

How to Approach the Question

First, carefully read the problem and identify all the given values: train speed, time to cross a point object, and length of the platform.
Check for consistency in units. Here, the speed is in km/hr, while time is in seconds and length is in meters (after correcting the typo). Convert all units to a consistent system (e.g., meters and seconds).
Recognize that a 250 km platform is unrealistic and likely a typo for 250 m. State this assumption clearly.
Break the problem into two parts. First, use the information about crossing the man to find the length of the train using the formula: Length = Speed × Time.
For the second part, calculate the total distance the train needs to cover to cross the platform, which is (Length of Train + Length of Platform).
Finally, calculate the required time by dividing the total distance by the train's speed: Time = Total Distance / Speed.

Concept Tested & Keywords

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Practise the full AIIMS CRE SNO - 2023

Attempt every question from this paper in a timed mock, then review the full solution for each one.