Train A of length 100 m crosses a pole in 4 seconds. Train B approaching towards train A with a speed of 15 m/sec crosses it in 9.1 seconds. Find the length of train B

Train A of length 100 m crosses a pole in 4 seconds. Train B approaching towards train A with a speed of 15 m/sec crosses it in 9.1 seconds. Find the length of train B
1). 264 m
2). 200 m
3). 250 m
4). 260 m

Train A of length $100$ m crosses a pole in $4$ seconds.
Speed of Train A:

$ \frac{100}{4} = 25 $ m/sec

Train B is approaching towards Train A with a speed of $15$ m/sec and crosses it in $9.1$ seconds.
Let the length of Train B be $x$ meters.

Since Train B crosses Train A, the relative speed of Train B with respect to Train A is:

$ 25 + 15 = 40 $ m/sec

Using the formula:

$ \text{Time} = \frac{\text{Total Distance}}{\text{Speed}} $

$ 9.1 = \frac{x + 100}{40} $

Multiplying both sides by $40$:

$ x + 100 = 9.1 \times 40 $

$ x + 100 = 364 $

$ x = 364 - 100 $

$ x = 264 $

Thus, the correct answer is:

$ \boxed{264} $

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