A train passes a telegraph post in 8 seconds and then passes completely over a bridge that is 264 metres long in 20 seconds. What is the speed of the train in km/h?

Introduction / Context:
This problem combines basic distance–speed–time relationships with the idea that a moving train must cover different effective distances when it passes a single point versus when it passes a bridge. It tests the ability to form and solve simple equations to find both the length of the train and its speed in km/h.

Given Data / Assumptions:

• Time to pass a telegraph post completely = 8 seconds.
• Time to cross a bridge that is 264 metres long = 20 seconds.
• The train runs at uniform speed in a straight line.
• We assume no delays or changes in speed between the two situations.
• We must find the speed of the train in km/h.

Concept / Approach:
When a train passes a single point such as a post, the distance covered is equal to the length of the train. When it passes a bridge, the distance covered is the sum of the length of the train and the length of the bridge. Let the length of the train be L metres and the speed be v metres per second. We use the relationship speed = distance / time in both scenarios, set up equations, solve for L, then compute v and convert to km/h using the factor 18 / 5.

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 post, L / v = 8, so v = L / 8.Step 3: When crossing the 264 metre bridge, the distance is L + 264 and time is 20 seconds, so (L + 264) / v = 20.Step 4: Substitute v = L / 8 into the second equation to get (L + 264) / (L / 8) = 20.Step 5: Simplify: 8 * (L + 264) / L = 20, so 8L + 2112 = 20L, giving 12L = 2112 and L = 176 metres.Step 6: Speed v = L / 8 = 176 / 8 = 22 metres per second.Step 7: Convert to km/h: speed in km/h = 22 * 18 / 5 = 79.2 km/h.

Verification / Alternative check:
Check with L = 176 metres and v = 22 metres per second.Time to pass post = 176 / 22 = 8 seconds, which agrees with the data.Time to cross bridge = (176 + 264) / 22 = 440 / 22 = 20 seconds, which also matches the given information.

Why Other Options Are Wrong:
Speeds such as 69.5 km/h, 70 km/h, 72 km/h or 79 km/h are all close but incorrect. They arise if one approximates during intermediate steps or uses a wrong conversion factor between metres per second and km/h. Only 79.2 km/h satisfies both time conditions exactly when back-substituted.

Common Pitfalls:
Candidates sometimes forget that the distance covered while crossing the bridge includes both the train length and the bridge length. Another typical mistake is incorrect algebra while solving for L and v, such as cross multiplying incorrectly. Errors in unit conversion, such as using 5 / 18 instead of 18 / 5 to convert metres per second to km/h, are also frequent. Working carefully through each step and checking dimensions helps avoid these issues.

Final Answer:
The speed of the train is 79.2 km/h.