The following questions are accompanied by two statements I and II. You have to determine which statements(s) is/are sufficient/ necessary to answer the questions.
What is the speed of train A running in opposite direction of train B?
I. Train B crosses a man standing in 10 sec. with 54 km/hr.
II. Length of train A is twice of length of train B.

Options

A. Statement i alone is sufficient to answer the question but statement II alone is not sufficient to answer the questions.
B. Statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question.
C. Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.
D. Neither statement I nor statement II by itself is sufficient to answer the question.

Answer

To solve the problem, we need to determine the speed of train A running in the opposite direction of train B using the provided statements.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to find the speed of train A, which is running in the opposite direction to train B.

2. **Analyzing Statement I**:
- Statement I states that "Train B crosses a man standing in 10 seconds with a speed of 54 km/hr."
- To find the length of train B (LB), we can use the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- Rearranging gives:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- Convert the time from seconds to hours:
\[ 10 \text{ seconds} = \frac{10}{3600} \text{ hours} = \frac{1}{360} \text{ hours} \]
- Now, substituting the values:
\[ LB = 54 \text{ km/hr} \times \frac{1}{360} \text{ hr} = \frac{54}{360} \text{ km} = \frac{3}{20} \text{ km} \]

3. **Analyzing Statement II**:
- Statement II states that "Length of train A is twice the length of train B."
- Therefore, we can express the length of train A (LA) as:
\[ LA = 2 \times LB = 2 \times \frac{3}{20} \text{ km} = \frac{6}{20} \text{ km} = \frac{3}{10} \text{ km} \]

4. **Combining the Information**:
- From Statement I, we have the speed of train B and its length.
- From Statement II, we have the length of train A.
- However, we still do not have any information about the speed of train A.

5. **Conclusion**:
- Since we do not have sufficient information to determine the speed of train A from either statement alone or even when combined, we conclude that:
- **Neither Statement I nor Statement II is sufficient to answer the question.**

### Final Answer:
The correct option is D: Neither statement alone is sufficient to answer the question.

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