A 540 m long train, running at a uniform speed, crosses a platfrom in 55 seconds and crosses a man stading on the platform in 36 seconds. What is the length (in cm) of the platform?

Options

A. 325
B. 400
C. 450
D. 285

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the speed of the train
The train crosses a man standing on the platform in 36 seconds. The length of the train is 540 meters.

**Formula:**
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

**Calculation:**
\[ \text{Speed} = \frac{540 \text{ m}}{36 \text{ s}} = 15 \text{ m/s} \]

### Step 2: Set up the equation for crossing the platform
Let the length of the platform be \( x \) meters. When the train crosses the platform, it covers a distance equal to the length of the train plus the length of the platform.

**Distance covered while crossing the platform:**
\[ \text{Distance} = \text{Length of train} + \text{Length of platform} = 540 + x \]

**Time taken to cross the platform:**
The train crosses the platform in 55 seconds.

### Step 3: Use the speed to find the equation
Using the speed we calculated and the time taken to cross the platform, we can set up the equation:

**Formula:**
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

**Substituting the values:**
\[ 540 + x = 15 \text{ m/s} \times 55 \text{ s} \]

### Step 4: Calculate the right side of the equation
**Calculation:**
\[ 540 + x = 825 \]

### Step 5: Solve for \( x \)
Now, we can isolate \( x \):

**Rearranging the equation:**
\[ x = 825 - 540 \]

**Calculation:**
\[ x = 285 \text{ m} \]

### Step 6: Convert the length of the platform to centimeters
Since the question asks for the length of the platform in centimeters, we convert meters to centimeters (1 m = 100 cm):

**Calculation:**
\[ x = 285 \text{ m} \times 100 = 28500 \text{ cm} \]

### Final Answer:
The length of the platform is **28500 cm**.

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