A train travelling at a speed of 30 m/sec crosses a platform, 600 meters long, in 30 seconds. The length (in meters) of train is

Options

A. 120
B. 150
C. 200
D. 300

Answer

To solve the problem of finding the length of the train, we can follow these steps:

### Step 1: Understand the problem
We know that a train is crossing a platform that is 600 meters long, and it takes 30 seconds to completely cross the platform. The speed of the train is given as 30 m/sec.

### Step 2: Calculate the total distance covered
When the train crosses the platform, it covers the length of the train plus the length of the platform. Therefore, the total distance covered by the train while crossing the platform can be expressed as:
\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Platform} \]
Let the length of the train be \( X \) meters. Thus, the total distance covered is:
\[ X + 600 \]

### Step 3: Use the formula for distance
We know that distance can also be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Given that the speed of the train is 30 m/sec and the time taken to cross the platform is 30 seconds, we can calculate the distance:
\[ \text{Distance} = 30 \, \text{m/sec} \times 30 \, \text{sec} = 900 \, \text{meters} \]

### Step 4: Set up the equation
Now we can set up the equation based on the total distance covered:
\[ X + 600 = 900 \]

### Step 5: Solve for \( X \)
To find the length of the train \( X \), we can rearrange the equation:
\[ X = 900 - 600 \]
\[ X = 300 \]

### Step 6: Conclusion
The length of the train is 300 meters.

### Final Answer:
The length of the train is **300 meters**.

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