Time and Distance [समय और दूरी] - 01

Question:  A train running at 25 km/hr takes 18 seconds to pass a platform. Next it takes 12 seconds to pass a man walking at 5 km/hr in the opposite direction. Find the length of the platform. [25 किमी/घंटे की चाल से चल रही एक ट्रेन, एक प्लेटफार्म को 18 सेकेण्ड में पार कर लेती है. फिर, वही ट्रेन 5 किमी/घंट की चाल से, विपरीत दिशा से आ रहे एक व्यक्ति को 12 सेकेण्ड में पार करती है; तो बताएँ कि प्लेटफार्म की लम्बाई कितनी है?]  [Ans. (c) 25 m]

(a) 24 m  (b) 42 m (c) 25 m  (d) 22 m (e) None of these 

Detailed  solution: When a train crosses a man, it means it describes a distance equal to its length in that given time. But, when a train crosses a platform, it means it describes a distance equal to the sum of the lengths of the train and platform.

Since here, the train running at 25 km/hr takes 18 seconds to pass a platform, so

Sum of the length of the train and platform = [25×(5/18)] m/s×18 s = 125 m

Again, this train takes 12 seconds to pass a man walking at 5 km/hr in the opposite direction. So, the relative speed of the train is (25 + 5) km/h = 30 km/h

Length of the train = [30×(5/18) ]) m/s×12 s = 100 m

Therefore, the length of the platform = (125 – 100) m = 25 m Ans.