Train X crosses a stationary train Y in 60 seconds and crosses a pole in 25 seconds at the same constant speed. If the length of train X is 300 metres, what is the length of stationary train Y in metres?

Introduction / Context:
Here we compare how a moving train crosses a stationary train and a fixed pole. Crossing a pole reveals the speed of train X because only its own length matters. Crossing a stationary train requires train X to cover the combined length of both trains. By using the same speed and the different times, we can determine the length of train Y.

Given Data / Assumptions:

• Train X length = 300 m.
• Train X crosses a pole in 25 s.
• Train X crosses stationary train Y in 60 s.
• Train Y is stationary.
• Speed of train X is constant throughout.

Concept / Approach:
When a train crosses a pole, distance = length of the train, so we can find its speed from length and time. When it crosses another stationary train, the required distance is length of X plus length of Y. Time and speed are known, so we can solve for the length of Y. The key formulas are speed = distance / time and distance = speed * time.

Step-by-Step Solution:
Step 1: Speed of train X when crossing a pole = length / time = 300 / 25 = 12 m/s. Step 2: When crossing train Y, distance to be covered = length of X + length of Y. Step 3: Let length of Y be L metres. Step 4: Time to cross Y = 60 s, speed = 12 m/s. Step 5: Therefore, distance = speed * time = 12 * 60 = 720 m. Step 6: So 300 + L = 720. Step 7: Hence, L = 720 - 300 = 420 m.

Verification / Alternative check:
We can verify by using the derived lengths. If train X is 300 m and train Y is 420 m, total distance is 720 m. At 12 m/s, time required is 720 / 12 = 60 s, which matches the given crossing time. For the pole, 300 m at 12 m/s gives 25 s, confirming consistency with the original data.

Why Other Options Are Wrong:
Lengths like 360, 380, or 320 m would lead to total distances differing from 720 m, and thus crossing times different from 60 s at 12 m/s. The value 460 m also fails this check, as 300 + 460 = 760 m, which would require more than 60 seconds to cross at the same speed.

Common Pitfalls:
A frequent error is to consider only one of the train lengths when crossing another train instead of summing both. Some learners may miscalculate the speed of train X or misapply the distance = speed * time relation. Keeping a clear distinction between pole crossing and train crossing scenarios is vital.

Final Answer:
The length of stationary train Y is 420 m.