The length of train A is 300 meters and it cross a 500 meters long platform in 30 seconds. If length of train B is two times of the length of train A and speed of train B is 198 km/hr, then find the time taken by train B to cross the platform (in seconds)?

The correct option is 20.

Step-by-Step Explanation:

Step 1: Find the length of train B.
We are given that the length of train A is 300 meters.
The length of train B is twice the length of train A:
$\text{Length of train B}=2\times \text{Length of train A}$
$\text{Length of train B}=2\times 300\text{m}=600\text{m}$

Step 2: Convert the speed of train B to meters per second (m/s).
The speed of train B is given as 198 km/hr.
To convert the speed from kilometers per hour (km/hr) to meters per second (m/s), we multiply it by $\frac{5}{18}$:
$\text{Speed of train B}=198\times \frac{5}{18}\text{m/s}$
$\text{Speed of train B}=11\times 5\text{m/s}=55\text{m/s}$

Step 3: Calculate the total distance train B needs to cover to cross the platform.
To completely cross the platform, train B must travel a distance equal to the sum of its own length and the length of the platform.
The length of the platform is 500 meters.
$\text{Total Distance}=\text{Length of train B}+\text{Length of platform}$
$\text{Total Distance}=600\text{m}+500\text{m}=1100\text{m}$

Step 4: Find the time taken by train B to cross the platform.
We use the basic formula relating distance, speed, and time:
$\text{Time}=\frac{\text{Total Distance}}{\text{Speed}}$
$\text{Time}=\frac{1100}{55}\text{seconds}$
$\text{Time}=20\text{seconds}$

Therefore, it takes train B 20 seconds to cross the platform.