Train K crosses a stationary Train L in 50 seconds and crosses a signal pole in 20 seconds while running at the same constant speed. If the length of Train K is 240 m, what is the length of Train L in metres?

Introduction / Context:
This question involves a moving train crossing both a stationary pole and a stationary train. It requires understanding that the time taken to cross a pole depends only on the length of the moving train, whereas the time taken to cross another train depends on the sum of their lengths. By combining these two pieces of information, we can find the unknown length of the stationary train.

Given Data / Assumptions:

• Train K length = 240 m.
• Train K crosses a pole in 20 s.
• Train K crosses stationary Train L completely in 50 s.
• Train L is stationary on a parallel track.
• Train K runs at constant speed during both events.

Concept / Approach:
First, we use the time taken by Train K to cross a pole to find its speed, since distance equals train length in that case. Then, using the same speed and the time taken to cross Train L, we determine the total distance covered while crossing Train L. That distance equals the sum of the lengths of the two trains, so subtracting the known length of Train K gives us the length of Train L.

Step-by-Step Solution:
Speed of Train K = distance / time when crossing pole. Speed = 240 m / 20 s = 12 m/s. Time to cross Train L = 50 s. Total distance covered while crossing Train L = speed * time = 12 * 50 = 600 m. Total distance = length of K + length of L. So, 600 = 240 + length of L. Length of Train L = 600 − 240 = 360 m.

Verification / Alternative check:
We can verify by reversing the logic. If Train L is 360 m long, the combined length is 240 + 360 = 600 m. At 12 m/s, time to cross this distance is 600 / 12 = 50 s, matching the information given. Therefore the answer is consistent.

Why Other Options Are Wrong:
Lengths like 60 m or 120 m yield total distances 300 m or 360 m, corresponding to crossing times of only 25 s or 30 s, which conflict with the given 50 s. A length of 240 m would make both trains 240 m each, total 480 m, leading to only 40 s. Only 360 m produces the correct 50 s crossing time.

Common Pitfalls:
Learners sometimes equate the distance travelled while crossing Train L to only the length of Train L, ignoring the length of Train K. Others may try to use km/h without converting units consistently. Remember that for train versus train, the relevant distance is the sum of their lengths, while for train versus pole it is only the train length.

Final Answer:
Hence, the length of stationary Train L is 360 m.