Each of these question have a questions followed by information given in three statements (1) (2) and (3). You have to study the question along with the information in three statements and decided that the information in which of the statement(s) is/are necessary to answer the question?
What is the speed of the train ?
The train crosses a signal pole in 14 secs.
The train crosses another train in 6 secs.
The train crosses a 200 metres long platform in 24 secs.

Options

A. Only 1 and 2
B. Only 1 and 3
C. Only 2 and 3
D. Any two of the three

Answer

To determine the speed of the train, we will analyze the information provided in the three statements step by step.

### Step 1: Analyze Statement 1
**Statement 1:** The train crosses a signal pole in 14 seconds.

- When the train crosses a signal pole, it travels a distance equal to its own length (let's denote the length of the train as \( L \)).
- The formula for speed is given by:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- Therefore, we can express the speed of the train as:
\[ \text{Speed} = \frac{L}{14} \]
- This gives us the relationship between the length of the train and its speed.

### Step 2: Analyze Statement 2
**Statement 2:** The train crosses another train in 6 seconds.

- When the train crosses another train, the distance covered is the sum of the lengths of both trains (let's denote the length of the other train as \( L_2 \)).
- The time taken is 6 seconds, so we can write:
\[ \text{Speed} = \frac{L + L_2}{6} \]
- This statement alone does not provide enough information to find the speed of the train without knowing the length of the other train.

### Step 3: Analyze Statement 3
**Statement 3:** The train crosses a 200 meters long platform in 24 seconds.

- When the train crosses a platform, the distance covered is the sum of the length of the train and the length of the platform.
- We can express this as:
\[ \text{Speed} = \frac{L + 200}{24} \]
- This gives us another equation relating the length of the train and its speed.

### Step 4: Combine Information
Now, we have the following equations from the statements:
1. From Statement 1: \( \text{Speed} = \frac{L}{14} \)
2. From Statement 2: \( \text{Speed} = \frac{L + L_2}{6} \) (not useful without \( L_2 \))
3. From Statement 3: \( \text{Speed} = \frac{L + 200}{24} \)

To find the speed of the train, we can use the first and third statements.

### Step 5: Solve for Speed
From Statement 1:
\[ \text{Speed} = \frac{L}{14} \quad \text{(1)} \]
From Statement 3:
\[ \text{Speed} = \frac{L + 200}{24} \quad \text{(2)} \]

Setting the two expressions for speed equal to each other:
\[ \frac{L}{14} = \frac{L + 200}{24} \]

Cross-multiplying gives:
\[ 24L = 14(L + 200) \]
Expanding the right side:
\[ 24L = 14L + 2800 \]
Rearranging gives:
\[ 24L - 14L = 2800 \]
\[ 10L = 2800 \]
\[ L = 280 \text{ meters} \]

Now substituting \( L \) back into either speed equation, let's use (1):
\[ \text{Speed} = \frac{280}{14} = 20 \text{ meters per second} \]

### Conclusion
The speed of the train is **20 meters per second**.