A 75 metre long train is moving at 20 kmph. It will cross a man standing on the platform in

Options

A. 12 second
B. 14 seconds
C. 13.5 seconds
D. 15.5 seconds

Answer

To solve the problem of how long it will take for a 75-meter long train moving at 20 km/h to cross a man standing on the platform, we can follow these steps:

### Step 1: Understand the Problem
The train needs to completely pass the man, which means it has to cover a distance equal to its own length (75 meters).

### Step 2: Convert Speed from km/h to m/s
The speed of the train is given in kilometers per hour (km/h). We need to convert this speed into meters per second (m/s) for easier calculations.

- **Conversion Formula**:
\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]

- **Calculation**:
\[ \text{Speed} = 20 \, \text{km/h} \times \frac{5}{18} = \frac{100}{18} \, \text{m/s} \approx 5.56 \, \text{m/s} \]

### Step 3: Use the Formula for Time
To find the time taken to cross the man, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
In this case, the distance is the length of the train (75 meters), and the speed is the converted speed (5.56 m/s).

### Step 4: Calculate Time
Substituting the values into the formula:
\[ \text{Time} = \frac{75 \, \text{meters}}{5.56 \, \text{m/s}} \approx 13.5 \, \text{seconds} \]

### Final Answer
The train will take approximately **13.5 seconds** to cross the man standing on the platform.

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