In each of the following questions there is a question which is followed by three statements. Read the question and all the three statements and then decide which of the statement(s) is/are sufficient to answer the question
What is the speed of the train?
The train crosses a railway signal pole in 13 seconds
The train passes a platform 250 m long in 27 seconds
The train crosses another train going in the same direction in 32 seconds

Options

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

Answer

To determine the speed of the train based on the provided statements, we will analyze each statement step by step.

### Step 1: Analyze Statement 1
**Statement 1:** The train crosses a railway signal pole in 13 seconds.

- When a train crosses a signal pole, the distance it covers is equal to its own length.
- Let the length of the train be \( L \) meters.
- The speed of the train can be calculated using the formula:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{L}{13} \]

### Step 2: Analyze Statement 2
**Statement 2:** The train passes a platform 250 m long in 27 seconds.

- When a train passes a platform, the distance covered is equal to the length of the train plus the length of the platform.
- Therefore, the distance covered is \( L + 250 \) meters.
- The speed can be calculated as:

\[ \text{Speed} = \frac{L + 250}{27} \]

### Step 3: Analyze Statement 3
**Statement 3:** The train crosses another train going in the same direction in 32 seconds.

- When two trains cross each other, the distance covered is equal to the sum of their lengths. However, since we do not know the length of the other train, we cannot derive a specific speed from this statement alone.
- Let the length of the other train be \( M \) meters. The distance covered is \( L + M \) meters, and the speed can be calculated as:

\[ \text{Speed} = \frac{L + M}{32} \]

### Step 4: Determine Sufficiency of Statements
Now, we need to determine if any of these statements alone or in combination can provide a unique solution for the speed of the train.

1. **Statement 1 alone:** Provides the speed in terms of the length of the train \( L \). Not sufficient.
2. **Statement 2 alone:** Provides the speed in terms of \( L \) and the platform length. Not sufficient.
3. **Statement 3 alone:** Does not provide enough information to determine the speed. Not sufficient.

### Step 5: Combine Statements
- **Combining Statement 1 and Statement 2:**
- From Statement 1: \( \text{Speed} = \frac{L}{13} \)
- From Statement 2: \( \text{Speed} = \frac{L + 250}{27} \)

Setting these two equations equal to each other:

\[ \frac{L}{13} = \frac{L + 250}{27} \]

Cross-multiplying gives:

\[ 27L = 13(L + 250) \]

Expanding and solving for \( L \):

\[ 27L = 13L + 3250 \]
\[ 14L = 3250 \]
\[ L = \frac{3250}{14} \approx 232.14 \text{ meters} \]

Now substituting \( L \) back into either speed equation to find the speed:

\[ \text{Speed} = \frac{L}{13} = \frac{232.14}{13} \approx 17.02 \text{ m/s} \]

### Conclusion
The speed of the train can be determined using Statements 1 and 2 together. Therefore, the answer is that Statements 1 and 2 together are sufficient to answer the question.