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.
Two trains X and Y starts from point A and B respectively towards each other. What is the distance between them when they start?
I. When both trains cross each other, time taken by train X to reach B is twice the time taken by train Y to reach A.
II. Distance between them after 60 min. is 800 km.

Options

A. Only I
B. Only II
C. Either I or II
D. Only I and II

Answer

To solve the problem, we need to analyze the two statements provided and determine if they are sufficient to answer the question about the distance between the two trains when they start from points A and B.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have two trains, X and Y, starting from points A and B, respectively, and moving towards each other. We need to find the distance between points A and B when they start.

2. **Analyzing Statement I**:
- Statement I states: "When both trains cross each other, the time taken by train X to reach B is twice the time taken by train Y to reach A."
- Let the time taken by train Y to reach A after they cross be \( t \). Then, the time taken by train X to reach B will be \( 2t \).
- This implies that the speed of train X is twice the speed of train Y. However, this statement alone does not provide a specific distance between A and B. We cannot determine the exact distance without additional information about the speeds or the time taken.

3. **Analyzing Statement II**:
- Statement II states: "The distance between them after 60 minutes is 800 km."
- This means that after one hour of travel, the two trains are 800 km apart. However, this statement alone does not give us the initial distance between A and B. It only tells us the distance after a certain time of travel.

4. **Combining Both Statements**:
- If we combine both statements, we can analyze the situation better.
- From Statement I, we know the relationship between the times taken by the trains. From Statement II, we know the distance between them after 60 minutes.
- Let’s denote the speed of train Y as \( v \). Then the speed of train X would be \( 2v \).
- In 60 minutes (1 hour), train Y would cover \( v \) km and train X would cover \( 2v \) km. The total distance covered by both trains in 1 hour would be \( v + 2v = 3v \).
- Since they are 800 km apart after 1 hour, we can set up the equation:
\[ \text{Initial Distance (A to B)} = 800 \text{ km} + 3v \]
- However, without knowing the speed \( v \), we cannot determine the exact distance between A and B.

5. **Conclusion**:
- Both statements together do not provide enough information to determine the initial distance between points A and B. Thus, we cannot answer the question based on the given statements.

### Final Answer:
- The answer is that both statements I and II together are insufficient to determine the distance between A and B.