A train moving with the speed of 24 km/hr crosses a platform in 10 minutes. If the length of the train and the platform is same then what is the length of the platform?

1. A

   2000 metres

2. B

   1200 metres

3. C

   1800 metres

4. D

   2400 metres

Appeared in: CIP Ranchi 2023

Explanation

• The fundamental principle is that when a train crosses a stationary object with length (like a platform), the total distance covered is the sum of the train's length and the object's length.
• Given that the length of the train and the platform are identical, let's denote this length as 'L'. The total distance the train travels to completely cross the platform is L + L = 2L.
• First, convert the speed to units consistent with the time and desired answer (metres and minutes). Speed = 24 km/hr = (24 × 1000 metres) / 60 minutes = 400 metres/minute.
• Next, calculate the total distance covered using the formula Distance = Speed × Time. Distance = 400 m/min × 10 min = 4000 metres.
• Finally, equate this distance to 2L: 2L = 4000 metres. Solving for L gives L = 2000 metres.

Why Other Options Were Wrong

• Option B: This value is incorrect and likely results from a calculation error, possibly in the speed conversion or the final division.
• Option C: This value does not match the calculated length. It may arise from an arithmetic mistake during multiplication or division.
• Option D: This value might be obtained if the speed was incorrectly calculated as 240 m/min (240 m/min * 10 min = 2400 m), which would then be incorrectly assumed as the final answer without dividing by 2.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Application of the formula Distance = Speed × Time in the context of relative motion, specifically a train crossing a platform as background academic context rather than a clinical decision trigger.
• While this is a mathematics question, the underlying skills are crucial in nursing. Accurate calculation is non-negotiable for medication dosage, IV drip rates, and interpreting patient data.
• This problem reinforces the importance of unit consistency. In clinical settings, converting between units (e.g., mg to mcg, lbs to kg) is a common task where errors can have serious consequences.
• What if? If the train were crossing a stationary point object (like a pole), the distance covered would simply be the length of the train (L). In that case, L would equal the total distance of 4000 metres.

How to Approach the Question

• First, identify all the given information: Speed = 24 km/hr, Time = 10 minutes.
• Recognize the key concept: When a train crosses a platform, the total distance covered is the sum of the train's length and the platform's length.
• Note the specific condition provided: Length of Train = Length of Platform. Let this be 'L'. Therefore, the total distance covered is 2L.
• Ensure all units are consistent before calculating. Convert the speed from km/hr to metres/minute to match the time unit and the units in the options.
• Calculate the total distance using the formula: Distance = Speed × Time.
• Set up the final equation (Total Distance = 2L) and solve for L to find the length of the platform.

Concept Tested & Keywords

• Concept Tested: Application of the formula Distance = Speed × Time in the context of relative motion, specifically a train crossing a platform.
• Stem keywords: train, speed, 24 km/hr, platform, 10 minutes, length
• Lead-in keywords: what is the length

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