A train crosses another train running in the opposite direction in x seconds. What is the speed of the train ?
I. Both the trains are running at the same speed.
II. The first train is y cm long.

Answer

To determine the speed of the train that crosses another train running in the opposite direction in x seconds, we need to analyze the information provided in the statements.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have two trains crossing each other. The time taken to cross each other is given as x seconds.
- We need to find the speed of one of the trains.

2. **Analyzing Statement I**:
- Statement I states that both trains are running at the same speed.
- Let the speed of each train be S.
- Since they are moving in opposite directions, the relative speed of the two trains is \( S + S = 2S \).
- The distance covered when the two trains cross each other is the sum of their lengths. If we denote the length of the first train as L1 and the second train as L2, the total distance is \( L1 + L2 \).
- The formula for speed is given by:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- Therefore, we can write:
\[ 2S = \frac{L1 + L2}{x} \]
- However, we do not have the lengths of the trains, so we cannot isolate S. Thus, Statement I alone is **not sufficient**.

3. **Analyzing Statement II**:
- Statement II states that the first train is y cm long.
- We know the length of the first train (L1 = y cm), but we do not know the length of the second train (L2).
- The total distance when the two trains cross each other is \( y + L2 \).
- Again, using the speed formula:
\[ \text{Relative Speed} = \frac{y + L2}{x} \]
- Without knowing L2, we cannot determine the speed of the first train. Thus, Statement II alone is **not sufficient**.

4. **Combining Both Statements**:
- From Statement I, we have \( 2S = \frac{L1 + L2}{x} \).
- From Statement II, we know \( L1 = y \), so we can substitute:
\[ 2S = \frac{y + L2}{x} \]
- However, we still do not know L2, which means we cannot solve for S. Thus, combining both statements is also **not sufficient**.

### Conclusion:
Neither statement alone nor the combination of both statements is sufficient to determine the speed of the train.

### Final Answer:
The answer is that **none of the statements are sufficient**.

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