A train passes two bridges of lengths 400 metre and 200 metre in 80 seconds and 60 seconds respectively. What is the length (in metre) of the train?

Options

A. 200
B. 400
C. 350
D. 720

Answer

To find the length of the train, we can set up two equations based on the information given about the time it takes for the train to pass two bridges.

### Step 1: Define Variables
Let \( L \) be the length of the train in meters.

### Step 2: Calculate Speed for Each Scenario
1. **For the first bridge (400 meters, 80 seconds)**:
- The total distance the train covers when passing the bridge is the length of the bridge plus the length of the train: \( 400 + L \).
- The speed of the train can be calculated as:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{400 + L}{80} \]

2. **For the second bridge (200 meters, 60 seconds)**:
- The total distance the train covers when passing this bridge is \( 200 + L \).
- The speed of the train can be calculated as:
\[ \text{Speed} = \frac{200 + L}{60} \]

### Step 3: Set Up the Equation
Since the speed of the train is the same in both cases, we can set the two expressions for speed equal to each other:
\[ \frac{400 + L}{80} = \frac{200 + L}{60} \]

### Step 4: Cross-Multiply to Eliminate Fractions
Cross-multiplying gives us:
\[ 60(400 + L) = 80(200 + L) \]

### Step 5: Distribute Both Sides
Distributing both sides results in:
\[ 24000 + 60L = 16000 + 80L \]

### Step 6: Rearrange the Equation
Now, rearranging the equation to isolate \( L \):
\[ 24000 - 16000 = 80L - 60L \]
\[ 8000 = 20L \]

### Step 7: Solve for \( L \)
Dividing both sides by 20 gives:
\[ L = \frac{8000}{20} = 400 \]

### Conclusion
The length of the train is \( 400 \) meters.