A train crosses a pole in 15 seconds and a platform 100 metres long in 25 seconds. Its length (in metres) is

Options

A. 50
B. 100
C. 150
D. 200

Answer

To find the length of the train, we can use the information provided about the time it takes for the train to cross a pole and a platform. Let's break down the solution step by step.

### Step-by-Step Solution:

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

2. **Calculate Speed When Crossing the Pole:**
When the train crosses a pole, the speed of the train can be expressed as:
\[ \text{Speed} = \frac{L}{15} \]
(since it takes 15 seconds to cross the pole).

3. **Calculate Speed When Crossing the Platform:**
When the train crosses a platform that is 100 meters long, the total distance covered is the length of the train plus the length of the platform. The speed can be expressed as:
\[ \text{Speed} = \frac{L + 100}{25} \]
(since it takes 25 seconds to cross the platform).

4. **Set the Two Speed Equations Equal:**
Since the speed of the train is the same in both cases, we can set the two equations equal to each other:
\[ \frac{L}{15} = \frac{L + 100}{25} \]

5. **Cross-Multiply to Eliminate Fractions:**
Cross-multiplying gives us:
\[ 25L = 15(L + 100) \]

6. **Distribute on the Right Side:**
Distributing the 15 on the right side:
\[ 25L = 15L + 1500 \]

7. **Rearrange the Equation:**
Subtract \( 15L \) from both sides:
\[ 25L - 15L = 1500 \]
This simplifies to:
\[ 10L = 1500 \]

8. **Solve for \( L \):**
Divide both sides by 10:
\[ L = 150 \]

9. **Conclusion:**
The length of the train is \( 150 \) meters.

### Final Answer:
The length of the train is **150 meters**.