The length of platform is double of the length oftrain. Speed ofthe train is 144 km/hr.If train crosses the platform in 30 seconds, then whatis the length of the platform?

Options

A. 600 metres
B. 800 metres
C. 500 metres
D. 400 metres

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Define Variables
Let the length of the train be \( L_T = X \). According to the problem, the length of the platform \( L_P \) is double the length of the train:
\[ L_P = 2X \]

### Step 2: Convert Speed to Meters per Second
The speed of the train is given as \( 144 \) km/hr. To convert this speed into meters per second, we use the conversion factor \( \frac{5}{18} \):
\[ \text{Speed in m/s} = 144 \times \frac{5}{18} = 40 \text{ m/s} \]

### Step 3: Determine the Total Distance Covered
When the train crosses the platform, it travels a distance equal to the length of the platform plus the length of the train:
\[ \text{Total Distance} = L_P + L_T = 2X + X = 3X \]

### Step 4: Use the Time Taken to Cross
The time taken by the train to cross the platform is given as \( 30 \) seconds. We can use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the known values:
\[ 3X = 40 \text{ m/s} \times 30 \text{ s} \]
\[ 3X = 1200 \text{ m} \]

### Step 5: Solve for \( X \)
Now, we can solve for \( X \):
\[ X = \frac{1200}{3} = 400 \text{ m} \]

### Step 6: Calculate the Length of the Platform
Now that we have the length of the train, we can find the length of the platform:
\[ L_P = 2X = 2 \times 400 = 800 \text{ m} \]

### Conclusion
The length of the platform is \( 800 \) meters.

### Final Answer
The answer to the question is \( 800 \) meters.

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