Train A passes a stationary train B in 24 seconds and passes a pole in 9 seconds. If the speed of train A is 48 km/h, what is the length (in metres) of train B?

Introduction / Context:
This question involves finding the length of a stationary train using information about how a moving train passes a pole and passes the stationary train. It uses the basic time, speed and distance relationship and the idea that when a train passes an object, the distance covered depends on what is being passed (a pole, a platform or another train).

Given Data / Assumptions:

• Speed of train A = 48 km/h.
• Time taken by train A to pass a pole = 9 seconds.
• Time taken by train A to pass stationary train B completely = 24 seconds.
• Train B is stationary on the track.

Concept / Approach:
First convert the speed of train A from km/h to m/s. Using the time to cross a pole, we can find the length of train A. Then, using the time taken to pass train B, we can find the combined length of both trains. Subtracting the length of train A from the combined length gives the length of train B.

Step-by-Step Solution:
Speed of train A in m/s = 48 * 1000 / 3600 = 48 * 5 / 18 = 40 / 3 m/s. When passing a pole, distance covered = length of train A. Length of train A = speed * time = (40 / 3) * 9 = 120 m. When passing train B, distance covered = length of A + length of B. Total distance in 24 s = (40 / 3) * 24 = 320 m. So length of B = 320 - 120 = 200 m.

Verification / Alternative check:
Check by reversing: length of A = 120 m, length of B = 200 m. When A passes B, total distance is 320 m. At speed 40 / 3 m/s, time = 320 / (40 / 3) = 24 s, matching the given time. So the computed length of train B is correct.

Why Other Options Are Wrong:

• 160 m and 180 m are both smaller than the correct value and do not satisfy the combined length calculation.
• 145 m also does not produce the given 24 seconds when substituted back.

Common Pitfalls:
Some learners forget to convert km/h to m/s, which leads to incorrect lengths. Others mistakenly consider only one train when computing the distance for the 24 second interval, rather than the sum of both trains' lengths. Careful unit conversion and understanding of what distance is covered in each scenario are crucial.

Final Answer:
The length of the stationary train B is 200 m.