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A train runs at a speed of 45 km/hr. It can cross a platform of length 400 metres in 40 seconds. By how much should it increase its speed so as to cross a bridge of length 500 metres in 30 seconds (in m/sec)?

A train runs at a speed of 45 km/hr. It can cross a platform of length 400 metres in 40 seconds. By how much should it increase its speed so as to cross a bridge of length 500 metres in 30 seconds (in m/sec)? Correct Answer 7.5

Speed of train = 45 km/hr = 45 × (5/18) m/sec = 12.5 m/sec

Let length of train be N metres.

Time taken to cross the platform = (length of the train + length of the platform)/speed of the train

⇒ 40 = (N + 400)/12.5

⇒ N = 500 – 400 = 100

Length of train is 100 metres.

Suppose the train increases its speed by T m/sec.

Time taken to cross the bridge = (length of train + length of bridge)/speed of train

⇒ 30 = (100 + 500)/(12.5 + T)

⇒ 375 + 30T = 600

⇒ T = 225/30 = 7.5

∴ Speed should be increased by 7.5 m/sec.

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