A train passes two bridges of lengths 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is :

Options

A. 80 m
B. 90 m
C. 200 m
D. 150 m

Answer

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

### Step-by-step Solution:

1. **Define Variables**:
Let the length of the train be \( X \) meters.

2. **Calculate Distance for Each Bridge**:
- For the first bridge (800 m), the total distance the train covers is \( X + 800 \) meters.
- For the second bridge (400 m), the total distance is \( X + 400 \) meters.

3. **Use the Formula for Speed**:
Speed is defined as distance divided by time. Since the speed of the train is constant, we can set up the following equations:
- For the first bridge:
\[ \text{Speed} = \frac{X + 800}{100} \]
- For the second bridge:
\[ \text{Speed} = \frac{X + 400}{60} \]

4. **Set the Speeds Equal**:
Since the speed is constant, we can equate the two expressions:
\[ \frac{X + 800}{100} = \frac{X + 400}{60} \]

5. **Cross Multiply to Solve for \( X \)**:
Cross multiplying gives:
\[ 60(X + 800) = 100(X + 400) \]

6. **Expand Both Sides**:
Expanding both sides results in:
\[ 60X + 48000 = 100X + 40000 \]

7. **Rearrange the Equation**:
Move all terms involving \( X \) to one side and constant terms to the other side:
\[ 48000 - 40000 = 100X - 60X \]
Simplifying gives:
\[ 8000 = 40X \]

8. **Solve for \( X \)**:
Divide both sides by 40:
\[ X = \frac{8000}{40} = 200 \]

9. **Conclusion**:
The length of the train is \( 200 \) meters.

### Final Answer:
The length of the train is **200 meters**.