Two trains A and B of length 400 m and (400 + x) m respectively are moving with same speed. If train A and B crosses a pole in 16 sec and 24 secs respectively then in what time train ‘B’ will cross 400 m long platform?

Correct Answer: The correct option is 40 sec.

Let us break down the solution step-by-step:

Step 1: Find the speed of the trains
We are given that Train A of length 400 m crosses a pole in 16 seconds. When a train crosses a pole, the distance covered is equal to the length of the train.
Since speed is equal to distance divided by time, we can calculate the speed of Train A as:

$\text{Speed of Train A}=\frac{\text{Length of Train A}}{\text{Time taken}}=\frac{400}{16}=25\text{m/s}$

Since both Train A and Train B are moving at the same speed, the speed of Train B is also 25 m/s.

Step 2: Find the length of Train B
We are given that Train B crosses the pole in 24 seconds at the same speed of 25 m/s. The distance covered while crossing the pole is the length of Train B itself:

$\text{Length of Train B}=\text{Speed}\times \text{Time}=25\times 24=600\text{m}$

Step 3: Calculate the time taken by Train B to cross the platform
When Train B crosses a 400 m long platform, the total distance it needs to cover is the sum of the length of the train and the length of the platform:

$\text{Total Distance}=\text{Length of Train B}+\text{Length of Platform}=600+400=1000\text{m}$

Using the speed of Train B (25 m/s), we find the time taken to cross the platform:

$\text{Time Taken}=\frac{\text{Total Distance}}{\text{Speed}}=\frac{1000}{25}=40\text{seconds}$

Therefore, Train B will cross the platform in 40 sec.