What is the speed of a running train which takes 6 seconds to cross a signal post ?
I. The length of the train is 90 m.
II. The trains takes 18 seconds to cross a platform 180 m long.

Answer

To solve the question, we will analyze the information provided in both statements and use the formula for speed, which is:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

### Step 1: Analyze Statement I
**Statement I:** The length of the train is 90 m.

When the train crosses a signal post, the distance it covers is equal to its own length. Therefore, the distance is 90 m, and the time taken to cross the signal post is given as 6 seconds.

Using the formula for speed:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{90 \text{ m}}{6 \text{ s}} = 15 \text{ m/s} \]

### Step 2: Analyze Statement II
**Statement II:** The train takes 18 seconds to cross a platform 180 m long.

When the train crosses a platform, the total distance covered is the sum of the lengths of the train and the platform. Therefore, the distance is:

\[ \text{Distance} = \text{Length of Train} + \text{Length of Platform} = 90 \text{ m} + 180 \text{ m} = 270 \text{ m} \]

Now, using the time taken to cross the platform (18 seconds), we can find the speed:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{270 \text{ m}}{18 \text{ s}} = 15 \text{ m/s} \]

### Conclusion
From both statements, we find that the speed of the train is consistently calculated as 15 m/s.

### Final Answer
The speed of the running train is **15 m/s**.

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