A train moving with uniform speed passes a pole in 10 sec and a bridge of length 1200 m in 130 sec. speed of the train is :

Options

A. 90 km/hr
B. 72 km/hr
C. 36 km/hr
D. 54 km/hr

Explanation

To find the speed of the train, we can break down the problem into a few steps:

### Step 1: Define Variables
Let:
- \( L \) = Length of the train (in meters)
- \( V \) = Speed of the train (in meters per second)
- \( T_1 = 10 \) seconds (time taken to pass the pole)
- \( T_2 = 130 \) seconds (time taken to pass the bridge)
- Length of the bridge = 1200 meters

### Step 2: Write the First Equation
When the train passes the pole, it travels a distance equal to its own length \( L \) in \( T_1 \) seconds. Thus, we can write the equation:
\[ L = V \times T_1 \]
Substituting \( T_1 \):
\[ L = V \times 10 \quad \text{(1)} \]

### Step 3: Write the Second Equation
When the train passes the bridge, it travels a distance equal to the length of the train plus the length of the bridge in \( T_2 \) seconds. Thus, we can write the equation:
\[ L + 1200 = V \times T_2 \]
Substituting \( T_2 \):
\[ L + 1200 = V \times 130 \quad \text{(2)} \]

### Step 4: Substitute Equation (1) into Equation (2)
From Equation (1), we have \( L = 10V \). We can substitute this into Equation (2):
\[ 10V + 1200 = 130V \]

### Step 5: Solve for \( V \)
Rearranging the equation gives:
\[ 1200 = 130V - 10V \]
\[ 1200 = 120V \]
Now, divide both sides by 120:
\[ V = \frac{1200}{120} = 10 \text{ m/s} \]

### Step 6: Convert Speed to Kilometers per Hour
To convert the speed from meters per second to kilometers per hour, we use the conversion factor \( \frac{18}{5} \):
\[ V_{km/h} = V_{m/s} \times \frac{18}{5} \]
Substituting \( V = 10 \):
\[ V_{km/h} = 10 \times \frac{18}{5} = 36 \text{ km/h} \]

### Final Answer
The speed of the train is \( 36 \text{ km/h} \).

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