A 250 m long train overtakes a man moving at a speed of 7 km/h (in same direction) in 36 seconds. How much time (in seconds) will it take this train to completely cross another 415 m long train, moving in the opposite direction at a speed of 82 km/h?

Given:

A 250 m long train overtakes a man moving at a speed of 7 km/h (in same direction) in 36 seconds.

Another 415 m long train is moving in the opposite direction at a speed of 82 km/h.

Formula used:

Relative Speed (same direction) = Speed of Train - Speed of Man

Speed = Distance / Time

Relative Speed (opposite direction) = Speed of Train + Speed of Another Train

Time to cross = Total Distance / Relative Speed

Calculation:

First, find the speed of the train:

Let the speed of the train be x km/h.

Relative Speed (same direction) = x - 7 km/h.

Distance = 250 m = 0.25 km.

Time = 36 seconds = 36/3600 hours = 0.01 hours.

Speed = Distance / Time

⇒ x - 7 = 0.25 / 0.01

⇒ x - 7 = 25

⇒ x = 32 km/h

Next, find the time to cross the other train:

Relative Speed (opposite direction) = 32 + 82 = 114 km/h.

Total Distance = 250 m + 415 m = 665 m = 0.665 km.

Time to cross = Total Distance / Relative Speed

⇒ Time = 0.665 / 114

⇒ Time = 0.00583 hours

⇒ Time = 0.00583 × 3600 seconds

⇒ Time ≈ 21 seconds

∴ The correct answer is option (4).