A 500 m long goods train crosses a platform in 36 seconds. If the length of the platform is 220 m. then what is the speed of the goods train in know ?

Options

A. 60
B. 72
C. 80
D. 85

Answer

To find the speed of the goods train, we can follow these steps:

### Step 1: Identify the lengths
- Length of the goods train = 500 m
- Length of the platform = 220 m

### Step 2: Calculate the total distance covered by the train
When the train crosses the platform, it covers its own length plus the length of the platform. Therefore, the total distance (D) covered by the train is:
\[ D = \text{Length of train} + \text{Length of platform} \]
\[ D = 500 \, \text{m} + 220 \, \text{m} = 720 \, \text{m} \]

### Step 3: Identify the time taken to cross the platform
The time (T) taken to cross the platform is given as:
\[ T = 36 \, \text{seconds} \]

### Step 4: Calculate the speed of the train
Speed (S) is calculated using the formula:
\[ S = \frac{D}{T} \]
Substituting the values we found:
\[ S = \frac{720 \, \text{m}}{36 \, \text{s}} \]
\[ S = 20 \, \text{m/s} \]

### Step 5: Convert the speed from meters per second to kilometers per hour
To convert the speed from meters per second (m/s) to kilometers per hour (km/h), we use the conversion factor \( \frac{18}{5} \):
\[ \text{Speed in km/h} = S \times \frac{18}{5} \]
Substituting the speed we calculated:
\[ \text{Speed in km/h} = 20 \, \text{m/s} \times \frac{18}{5} \]
\[ \text{Speed in km/h} = 20 \times 3.6 = 72 \, \text{km/h} \]

### Final Answer
The speed of the goods train is **72 km/h**.

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