A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 264 metres long in 20 seconds. The length of the train (in metres) is

Options

A. 188
B. 176
C. 175
D. 96

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Define Variables
Let the length of the train be \( x \) meters.

### Step 2: Calculate Speed of the Train
The train passes a man standing on the platform in 8 seconds. The speed of the train can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Here, the distance is the length of the train \( x \) and the time is 8 seconds. Therefore, the speed of the train is:
\[ \text{Speed} = \frac{x}{8} \text{ m/s} \]

### Step 3: Calculate Total Distance when Crossing the Platform
The train crosses a platform that is 264 meters long in 20 seconds. When the train crosses the platform, it covers its own length plus the length of the platform. Thus, the total distance covered is:
\[ \text{Total Distance} = x + 264 \text{ meters} \]
The speed during this crossing can be calculated as:
\[ \text{Speed} = \frac{x + 264}{20} \text{ m/s} \]

### Step 4: Set the Speeds Equal
Since both expressions represent the speed of the same train, we can set them equal to each other:
\[ \frac{x}{8} = \frac{x + 264}{20} \]

### Step 5: Cross-Multiply to Solve for \( x \)
Cross-multiplying gives us:
\[ 20x = 8(x + 264) \]

### Step 6: Expand and Simplify
Expanding the right side:
\[ 20x = 8x + 2112 \]
Now, subtract \( 8x \) from both sides:
\[ 20x - 8x = 2112 \]
\[ 12x = 2112 \]

### Step 7: Solve for \( x \)
Now, divide both sides by 12 to find \( x \):
\[ x = \frac{2112}{12} = 176 \]

### Conclusion
The length of the train is \( 176 \) meters.