Multiple choice

The numericle value of the speed of a train in km/hr is double of the time taken by it to cross a platform while it crosses a platform in 30 seconds. If the length of the train be 200 metres, then the length ( in metres) of the platform is एक ट्रेन की चाल का आंकिक मान किमी/घंण्टा में उस समय का दों गुना है जो एक प्लेटफार्म को पार करने में लगता है। जबकि यह प्लेटफार्म को 30 सेकेण्ड में पार करती है | यदि ट्रेन की लम्बाई 200 मीटर है, तो प्लेटफार्म की लम्बाई (मी. में) है -

  1. 400

  2. 300

  3. 200

  4. 500
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B Correct answer
Explanation

Let time taken to cross platform = t seconds. Speed = 2t km/hr = (2t × 5/18) m/s. Distance to cross platform = train length + platform length = 200 + L. Time = distance/speed, so 30 = (200 + L) / (2t × 5/18). But t = 30 seconds (given), so speed = 60 km/hr = 60 × 5/18 = 50/3 m/s. Distance = speed × time = (50/3) × 30 = 500m. So L = 500 - 200 = 300m. The key insight is that the numeric value of speed in km/hr equals the time in seconds.

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