A train passes two bridges of length 600 metres and 300 metres in 120 seconds and 80 seconds respectively. What is the length (in metres) of the train?

Options

A. A)200
B. B)250
C. C)300
D. D)450

Answer

To find the length of the train, we can follow these steps:

### Step 1: Understand the Problem
The train crosses two bridges of different lengths in different times. We need to find the length of the train.

### Step 2: Define Variables
Let:
- \( L \) = Length of the train (in meters)
- \( L_1 \) = Length of the first bridge = 600 meters
- \( L_2 \) = Length of the second bridge = 300 meters
- \( T_1 \) = Time taken to cross the first bridge = 120 seconds
- \( T_2 \) = Time taken to cross the second bridge = 80 seconds

### Step 3: Write the Distance Equation
When the train crosses a bridge, the distance covered is equal to the length of the train plus the length of the bridge. Therefore, we have:
1. For the first bridge:
\[ \text{Distance}_1 = L + L_1 = L + 600 \]
2. For the second bridge:
\[ \text{Distance}_2 = L + L_2 = L + 300 \]

### Step 4: Relate Distance, Speed, and Time
The speed of the train can be expressed as:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Thus, we can write:
1. For the first bridge:
\[ \text{Speed}_1 = \frac{L + 600}{120} \]
2. For the second bridge:
\[ \text{Speed}_2 = \frac{L + 300}{80} \]

### Step 5: Set Up the Ratio of Speeds
Since the speed of the train remains constant, we can set up the ratio of the two speeds:
\[ \frac{L + 600}{120} = \frac{L + 300}{80} \]

### Step 6: Cross-Multiply to Solve for L
Cross-multiplying gives us:
\[ 80(L + 600) = 120(L + 300) \]
Expanding both sides:
\[ 80L + 48000 = 120L + 36000 \]

### Step 7: Rearrange the Equation
Rearranging the equation to isolate \( L \):
\[ 48000 - 36000 = 120L - 80L \]
\[ 12000 = 40L \]

### Step 8: Solve for L
Dividing both sides by 40:
\[ L = \frac{12000}{40} = 300 \]

### Conclusion
The length of the train is \( L = 300 \) meters.