A train speeds past a fixed pole in 15 seconds and passes completely over a platform that is 100 metres long in 25 seconds. What is the length of the train in metres?

Introduction / Context:
This is a classic train and platform question. It checks whether you can distinguish between the distance covered when a train passes a fixed point (such as a pole) and when it passes an extended object like a platform. It also tests your skill in forming equations from the standard speed, distance and time relationship.

Given Data / Assumptions:

• The train passes a pole in 15 seconds.
• The train passes a platform 100 metres long in 25 seconds.
• The train moves at constant speed along a straight track.
• We must find the length of the train in metres.

Concept / Approach:
When a train passes a pole, the distance travelled during that time is equal to the train's own length. When the same train passes a platform, the distance travelled is equal to the sum of the train length and the platform length. Let the length of the train be L metres and its speed be v metres per second. From the pole information we can express v in terms of L, substitute into the platform equation, and then solve for L.

Step-by-Step Solution:
Step 1: Let the train length be L metres and its speed be v metres per second.Step 2: From passing the pole, L / v = 15, so v = L / 15.Step 3: For the platform, total distance to be covered = L + 100 metres, and time taken = 25 seconds.Step 4: So (L + 100) / v = 25. Substitute v = L / 15.Step 5: This gives (L + 100) / (L / 15) = 25, which simplifies to 15 * (L + 100) / L = 25.Step 6: Multiply out: 15L + 1500 = 25L, so 1500 = 10L, hence L = 150 metres.

Verification / Alternative check:
If L = 150 metres, then speed v = L / 15 = 150 / 15 = 10 metres per second.Time to pass platform = (L + 100) / v = (150 + 100) / 10 = 250 / 10 = 25 seconds, which matches the given data.Time to pass pole = L / v = 150 / 10 = 15 seconds, also matching the information given.

Why Other Options Are Wrong:
50 metres or 120 metres are far too small; they would not satisfy both time conditions simultaneously. The value 200 metres is too large and leads to inconsistent times when checked back. The option marked as data inadequate is incorrect because there is enough information to solve uniquely for the train length using two equations in two variables.

Common Pitfalls:
Students sometimes forget to add the platform length to the train length while computing the distance during platform crossing. Another common error is to confuse the roles of time and speed in the equations or to cancel terms incorrectly. Writing each equation carefully and substituting step by step is the safest method.

Final Answer:
The length of the train is 150 metres.