Train A travels at a speed of 72 km/hr and crosses a 500-meter-long platform in 50 seconds. After crossing the platform, it encounters train B moving in the opposite direction at a speed of 54 km/hr. If both trains completely pass each other in 24 seconds, them find the length of the train B.

To find the length of train B, we can break down the problem into two distinct steps. First, we use the details of train A crossing a platform to determine its length. Second, we use the relative speed of both trains crossing each other in opposite directions to determine the length of train B.

Step 1: Find the length of train A
The speed of train A is given as 72 km/hr. We need to convert this speed into meters per second (m/s) because the length of the platform is in meters and the crossing time is in seconds.
To convert from km/hr to m/s, we multiply by $\frac{5}{18}$:
$\text{Speed of train A}=72\times \frac{5}{18}=20\text{m/s}$

When a train crosses a platform, the total distance it covers is equal to the sum of the length of the train and the length of the platform.
Let $L_A$ be the length of train A.
$\text{Total distance}=L_A+500$

Using the formula $\text{Distance}=\text{Speed}\times \text{Time}$:
$L_A+500=20\times 50$
$L_A+500=1000$
$L_A=1000-500=500\text{meters}$
So, the length of train A is 500 meters.

Step 2: Find the length of train B
Next, train A meets train B moving in the opposite direction.
The speed of train B is 54 km/hr. Let's convert this speed to m/s:
$\text{Speed of train B}=54\times \frac{5}{18}=15\text{m/s}$

Since the two trains are moving in opposite directions, their relative speed is the sum of their individual speeds:
$\text{Relative speed}=\text{Speed of A}+\text{Speed of B}=20+15=35\text{m/s}$

When two trains completely pass each other, the total distance covered is the sum of the lengths of both trains.
Let $L_B$ be the length of train B.
$\text{Total distance}=L_A+L_B=500+L_B$

Using the formula $\text{Distance}=\text{Relative speed}\times \text{Time}$ where the passing time is 24 seconds:
$500+L_B=35\times 24$
$500+L_B=840$
$L_B=840-500=340\text{meters}$

Therefore, the length of train B is 340 meters.