A train crosses a pole in 12 seconds and a bridge of length 170 metre in 36 seconds. Then the speed of the train is :

Options

A. 25.5 kmph
B. 30.75 kmph
C. 10.8 kmph
D. 32.45 kmph

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Determine the length of the train
When the train crosses a pole, it covers a distance equal to its own length in the time taken.

Let the length of the train be \( L \) meters.

The time taken to cross the pole is 12 seconds.

So, we can express the speed of the train as:
\[ \text{Speed} = \frac{L}{12} \]

### Step 2: Determine the total distance covered when crossing the bridge
When the train crosses a bridge, it covers a distance equal to the length of the train plus the length of the bridge.

The length of the bridge is given as 170 meters.

So, the total distance covered when crossing the bridge is:
\[ \text{Total Distance} = L + 170 \]

The time taken to cross the bridge is 36 seconds.

Thus, we can express the speed of the train as:
\[ \text{Speed} = \frac{L + 170}{36} \]

### Step 3: Set the two expressions for speed equal to each other
Since both expressions represent the speed of the train, we can set them equal:
\[ \frac{L}{12} = \frac{L + 170}{36} \]

### Step 4: Cross-multiply to solve for \( L \)
Cross-multiplying gives us:
\[ 36L = 12(L + 170) \]

Expanding the right side:
\[ 36L = 12L + 2040 \]

### Step 5: Rearranging the equation
Now, we can rearrange the equation to isolate \( L \):
\[ 36L - 12L = 2040 \]
\[ 24L = 2040 \]

### Step 6: Solve for \( L \)
Now, divide both sides by 24:
\[ L = \frac{2040}{24} = 85 \text{ meters} \]

### Step 7: Calculate the speed of the train
Now that we have the length of the train, we can substitute \( L \) back into either speed formula. We can use the first one:
\[ \text{Speed} = \frac{L}{12} = \frac{85}{12} \approx 7.08 \text{ m/s} \]

### Step 8: Convert speed from m/s to km/h
To convert the speed from meters per second to kilometers per hour, we use the conversion factor:
\[ \text{Speed in km/h} = \text{Speed in m/s} \times \frac{18}{5} \]
\[ \text{Speed in km/h} = 7.08 \times \frac{18}{5} = 25.5 \text{ km/h} \]

### Final Answer
Thus, the speed of the train is **25.5 km/h**.

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