A train 150 metre long takes 20 seconds to cross a platform 450 metre long. The speed of the train in km per hour, is

Options

A. 108
B. 100
C. 106
D. 104

Answer

To solve the problem step by step, we need to find the speed of the train in kilometers per hour. Here’s how we can do it:

### Step 1: Calculate the Total Distance
The total distance the train travels while crossing the platform is the sum of the lengths of the train and the platform.

- Length of the train = 150 meters
- Length of the platform = 450 meters

**Total Distance = Length of Train + Length of Platform**
\[ \text{Total Distance} = 150 \, \text{m} + 450 \, \text{m} = 600 \, \text{m} \]

### Step 2: Use the Formula for Speed
We know the formula for speed is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

From the problem, we have:
- Distance = 600 meters
- Time = 20 seconds

**Calculating Speed:**
\[ \text{Speed} = \frac{600 \, \text{m}}{20 \, \text{s}} = 30 \, \text{m/s} \]

### Step 3: Convert Speed to Kilometers per Hour
To convert the speed from meters per second to kilometers per hour, we use the conversion factor:
- 1 km = 1000 m
- 1 hour = 3600 seconds

**Conversion Formula:**
\[ \text{Speed in km/h} = \text{Speed in m/s} \times \frac{3600}{1000} \]

**Calculating Speed in km/h:**
\[ \text{Speed in km/h} = 30 \, \text{m/s} \times \frac{3600}{1000} \]
\[ \text{Speed in km/h} = 30 \times 3.6 = 108 \, \text{km/h} \]

### Final Answer
The speed of the train is **108 km/h**.

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