Two friends X and Y start running towards each other at the same time from points A and B respectively and meet after 135 minutes. At what speed is X running ?
I. Point B is 45 km away from point A and speed of X is `150%` of the speed of Y.
II. Distance covered by Y was 18 km.

Options

A. if the data in Statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer to question.
B. if the data in statement Ii alone are sufficient to answer the questin, while the data in statemetn I alone are not suffcient to answer the question.
C. if data either in statement I alone or in statement II alone are sufficient to answer the question.
D. if the data in both statements I and II together are not sufficient to answer the question.

Explanation

To solve the problem, we need to determine the speed of friend X based on the information provided in the two statements. Let's analyze each statement step by step.

### Step 1: Understand the Problem
We have two friends, X and Y, running towards each other from points A and B respectively, and they meet after 135 minutes. We need to find the speed of X.

### Step 2: Convert Time
First, we convert the time from minutes to hours:
- 135 minutes = 135/60 = 2.25 hours (or 2 hours and 15 minutes).

### Step 3: Analyze Statement I
**Statement I:** Point B is 45 km away from point A and the speed of X is 150% of the speed of Y.

Let the speed of Y be \( v_Y \) km/h. Then the speed of X is:
\[ v_X = 1.5 \times v_Y \]

The total distance covered by both X and Y when they meet is 45 km. The time taken to meet is 2.25 hours.

Using the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

The combined distance covered by both X and Y is:
\[ v_X \times 2.25 + v_Y \times 2.25 = 45 \]

Substituting \( v_X \):
\[ (1.5 v_Y) \times 2.25 + v_Y \times 2.25 = 45 \]

Factoring out \( 2.25 \):
\[ 2.25 (1.5 v_Y + v_Y) = 45 \]
\[ 2.25 (2.5 v_Y) = 45 \]

Dividing both sides by 2.25:
\[ 2.5 v_Y = \frac{45}{2.25} \]
\[ 2.5 v_Y = 20 \]
\[ v_Y = \frac{20}{2.5} = 8 \text{ km/h} \]

Now, we can find the speed of X:
\[ v_X = 1.5 \times 8 = 12 \text{ km/h} \]

### Step 4: Analyze Statement II
**Statement II:** Distance covered by Y was 18 km.

From this statement alone, we know the distance covered by Y, but we do not have information about the speed of Y or the time taken. Therefore, we cannot determine the speed of X from this statement alone.

### Conclusion
From Statement I, we were able to determine the speed of X as 12 km/h. However, Statement II does not provide sufficient information to find the speed of X.

Thus, the answer is that **only Statement I is sufficient** to answer the question, while Statement II is not.

### Final Answer
The speed of X is **12 km/h**. Only Statement I is sufficient.

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