A train crosses a platform in 30 seconds travelling with a speed of 60 km/h. If the length of the train be 200 metres, then the length (in metres) of the platform is

Options

A. 400
B. 300
C. 200
D. 500

Answer

To solve the problem of finding the length of the platform that a train crosses in 30 seconds while traveling at a speed of 60 km/h, we can follow these steps:

### Step 1: Convert the speed from km/h to m/s
The speed of the train is given as 60 km/h. To convert this to meters per second (m/s), we use the conversion factor:
\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]
So,
\[ \text{Speed} = 60 \times \frac{5}{18} = \frac{300}{18} = \frac{50}{3} \text{ m/s} \]

### Step 2: Calculate the total distance covered by the train
The train crosses both the platform and its own length. Let \( x \) be the length of the platform in meters. The total distance covered when the train crosses the platform is:
\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Platform} = 200 + x \text{ meters} \]

### Step 3: Use the formula for distance
We know that distance can also be expressed as:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Here, the time taken to cross the platform is given as 30 seconds. Therefore, we can write:
\[ 200 + x = \left(\frac{50}{3}\right) \times 30 \]

### Step 4: Calculate the right-hand side
Calculating the right-hand side:
\[ \left(\frac{50}{3}\right) \times 30 = \frac{50 \times 30}{3} = \frac{1500}{3} = 500 \text{ meters} \]

### Step 5: Set up the equation
Now we have:
\[ 200 + x = 500 \]

### Step 6: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = 500 - 200 = 300 \text{ meters} \]

### Conclusion
The length of the platform is \( 300 \) meters.