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A train crosses a man standing on the sideways of railway track and a 600 m long railway platform in 40 seconds and 70 seconds respectively. What would be the time taken by train to cross a 100 m long bridge if its speed would be three-fifth of the current speed?

A train crosses a man standing on the sideways of railway track and a 600 m long railway platform in 40 seconds and 70 seconds respectively. What would be the time taken by train to cross a 100 m long bridge if its speed would be three-fifth of the current speed? Correct Answer 75 seconds

Given:

The time is taken by train to cross a man standing on the sideways of railway track = 40 seconds

The time is taken by train to cross railway platform = 70 seconds

Length of the platform = 600m 

Formula used:

Time is taken to cross a platform or bridge = (Sum of the length of train and bridge or platform)/(Speed of the train)

Calculation:

Let the length of the train is Y m.

Speed of train = length of the train/Time taken by train to cross the man

= (Y/40) m/sec

Now, speed of train = (length of train + length of platform) / time taken to cross the platform

⇒ Y/40 = (Y + 600)/70

⇒ 70Y = 40Y + 24000

⇒ 70Y – 40Y = 24000

⇒ 30Y = 24000

⇒ Y = 800 m

Hence, speed of train = 800/40

= 20 m/sec

Three-fifth of the speed = 20 × (3/5) = 12 m/sec

Time taken to cross 100 m long bridge = (length of bridge + length of train)/(speed of train)

⇒ Required time = (100 + 800)/12 = 900/12 = 75 seconds

∴ Required time is 75 seconds

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