1.

A person standing on a railway platform noticed that a train took 21 seconds to completely pass through the platform which was 84 m long and it took 9 seconds in passing him. The speed of the train was (a) 25.2 km/hr (b) 32.4 km/hr (c) 50.4 km/hr (d) 75.6 km/hr

Answer»

(a) 25.2 km/hr

Let the length of the train be x metres. Then, Speed of the train in passing through the platform = \(\frac{x+84}{21}\) m/sec and speed of the train in passing the man = \(\frac{x}{9}\) m/sec

Since both the speeds are the same,

\(\frac{x+84}{21}\) = \(\frac{x}{9}\) ⇒ 9\(x\) + 756 = 21\(x\)

⇒ 12\(x\) = 756 

⇒ \(x\) = \(\frac{756}{12}\) = 63 m

∴ Speed of the train = \(\frac{(63+84)}{21}\) m/sec = 7 m/sec

\(7\times\frac{18}{5}\) km/hr = 25.2 km/hr.



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