A train can cross a pole in 15 seconds and travelling at the same speed it can cross a bridge of 500 m in 45 seconds, then find the length of the train?(in metre)

Options

A. 250
B. 300
C. 200
D. 240

Answer

To solve the problem step by step, we will use the information provided about the train crossing a pole and a bridge to find the length of the train.

### Step 1: Understand the problem
We know that:
- The train crosses a pole in 15 seconds.
- The train crosses a bridge of 500 meters in 45 seconds.

### Step 2: Define variables
Let:
- \( L \) = Length of the train (in meters)
- \( S \) = Speed of the train (in meters per second)

### Step 3: Calculate the speed of the train
When the train crosses a pole, it travels a distance equal to its own length \( L \) in 15 seconds. Therefore, we can express the speed \( S \) as:
\[ S = \frac{L}{15} \]

### Step 4: Calculate the total distance when crossing the bridge
When the train crosses the bridge, it travels a distance equal to the length of the train plus the length of the bridge (500 meters) in 45 seconds. Therefore, the total distance covered while crossing the bridge can be expressed as:
\[ \text{Distance} = L + 500 \]
The speed can also be expressed as:
\[ S = \frac{L + 500}{45} \]

### Step 5: Set the two expressions for speed equal to each other
Since both expressions represent the speed of the train, we can set them equal to each other:
\[ \frac{L}{15} = \frac{L + 500}{45} \]

### Step 6: Cross-multiply to eliminate the fractions
Cross-multiplying gives us:
\[ 45L = 15(L + 500) \]

### Step 7: Distribute and simplify
Distributing on the right side:
\[ 45L = 15L + 7500 \]
Now, subtract \( 15L \) from both sides:
\[ 45L - 15L = 7500 \]
\[ 30L = 7500 \]

### Step 8: Solve for \( L \)
Now, divide both sides by 30:
\[ L = \frac{7500}{30} = 250 \]

### Conclusion
The length of the train is \( 250 \) meters.