1.

A train travelling at 36 km/hr passes in 12 seconds another train half its length, travelling in the opposite direction at 54 km/hr. If it also passes a railway platform in \(1\frac12\) minutes, what is the length of the platform? (a) 800 m (b) 700 m (c) 900 m (d) 1000 m

Answer»

(b) 700 m

Let the length of the first train be x metres. 

Then, length of the second train = \(\frac{x}{2}\) metres 

Relative speed = (36 + 54) km/hr = 90 km/h

= \(\big(90\times\frac5{18}\big)\) m/s = 25 m/s

∴ \(\frac{x+\frac{x}2}{25}=12\)  ⇒ \(\frac{3x}{2} = 300 \)  ⇒ \(x\) = 200.

∴ Length of the first train = 200 m. 

Let the length of the platform be y metres. 

Speed of the first train = \(\big(36\times\frac5{18}\big)\) m/s = 10 m/s

∴ (200 + y) x \(\frac1{10}\) = 90

⇒ 200 + y = 900 ⇒ y = 700 m.


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