A 400 metre long train crosses a 200 metre long platform. If the speed of train 30 km/hr, then what is the time taken (in seconds) to cross the platform?

Options

A. 70
B. 75
C. 72
D. 80

Answer

To solve the problem of how long it takes for a 400-meter long train to cross a 200-meter long platform at a speed of 30 km/hr, we can follow these steps:

### Step 1: Convert the speed from km/hr to m/s
The speed of the train is given as 30 km/hr. To convert this into meters per second (m/s), we use the conversion factor:

\[ \text{Speed in m/s} = \text{Speed in km/hr} \times \frac{5}{18} \]

Calculating this:

\[ \text{Speed in m/s} = 30 \times \frac{5}{18} = \frac{150}{18} = \frac{25}{3} \text{ m/s} \]

### Step 2: Calculate the total distance to be covered
The train needs to cross the entire length of the platform plus its own length. Therefore, the total distance (D) is:

\[ D = \text{Length of the train} + \text{Length of the platform} = 400 \text{ m} + 200 \text{ m} = 600 \text{ m} \]

### Step 3: Use the formula for time
The time (T) taken to cross the platform can be calculated using the formula:

\[ T = \frac{D}{\text{Speed}} \]

Substituting the values we have:

\[ T = \frac{600 \text{ m}}{\frac{25}{3} \text{ m/s}} = 600 \times \frac{3}{25} \]

### Step 4: Simplify the calculation
Calculating the above expression:

\[ T = \frac{1800}{25} = 72 \text{ seconds} \]

### Final Answer
The time taken for the train to cross the platform is **72 seconds**.

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