A moving train passes a platform 50 metre long in 14 seconds and a lamp post in 10 seconds. The speed of the train (in km/h) is

Options

A. 24
B. 36
C. 40
D. 45

Answer

To find the speed of the train in km/h, we will follow these steps:

### Step 1: Determine the length of the train
When the train passes the lamp post, it travels a distance equal to its own length in 10 seconds. Let the length of the train be \( L \) meters.

Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
For the lamp post:
\[ \text{Speed} = \frac{L}{10} \]

### Step 2: Determine the total distance when passing the platform
When the train passes the platform, it travels a distance equal to its own length plus the length of the platform (50 meters) in 14 seconds. Thus, the total distance is \( L + 50 \) meters.

Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
For the platform:
\[ \text{Speed} = \frac{L + 50}{14} \]

### Step 3: Set the two speed equations equal to each other
Since the speed of the train is the same in both cases, we can set the two equations equal to each other:
\[ \frac{L}{10} = \frac{L + 50}{14} \]

### Step 4: Cross-multiply to solve for \( L \)
Cross-multiplying gives:
\[ 14L = 10(L + 50) \]
Expanding the right side:
\[ 14L = 10L + 500 \]
Subtracting \( 10L \) from both sides:
\[ 4L = 500 \]
Dividing both sides by 4:
\[ L = 125 \text{ meters} \]

### Step 5: Calculate the speed of the train
Now that we have the length of the train, we can find the speed using the equation for the lamp post:
\[ \text{Speed} = \frac{L}{10} = \frac{125}{10} = 12.5 \text{ m/s} \]

### Step 6: Convert the speed from m/s to km/h
To convert from meters per second to kilometers per hour, we use the conversion factor \( 1 \text{ m/s} = 3.6 \text{ km/h} \):
\[ \text{Speed in km/h} = 12.5 \times 3.6 = 45 \text{ km/h} \]

### Final Answer
The speed of the train is **45 km/h**.

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