Given below in each question there are two statements (I) and (II). You must determine, which statement is enough to give the answer of question. Also, there are five alternatives given, you have to choose one alternative as your answer of the questions:
What is age of Rahul after 2 years.
I. Average age of Arun and Neeraj is 24 years and ratio of age of Rahul to Arun is 2:3.
II. Neeraj is 4 years elder than Satish and ratio of age of Satish to Rahul is 1:2

Options

A. only statementl
B. Only statement II
C. Both I and II together
D. Both statements together are not sufficient

Answer

To solve the problem, we need to analyze the two statements provided and determine if either one is sufficient to answer the question: "What is the age of Rahul after 2 years?"

### Step 1: Analyze Statement I
**Statement I:** The average age of Arun and Neeraj is 24 years, and the ratio of the age of Rahul to Arun is 2:3.

1. From the average age of Arun and Neeraj, we can find the total age of both:
\[ \text{Average} = \frac{\text{Age of Arun} + \text{Age of Neeraj}}{2} = 24 \]
Therefore,
\[ \text{Age of Arun} + \text{Age of Neeraj} = 24 \times 2 = 48 \text{ years} \]

2. Let the age of Arun be \( A \) and the age of Neeraj be \( N \). Thus, we have:
\[ A + N = 48 \]

3. The ratio of Rahul's age \( R \) to Arun's age \( A \) is given as:
\[ \frac{R}{A} = \frac{2}{3} \implies R = \frac{2}{3}A \]

4. We can substitute \( R \) in terms of \( A \) into the equation:
\[ R + A + N = R + 48 \]
We can find \( R \) if we find \( A \) or \( N \).

5. However, we still need to express \( A \) or \( N \) in terms of a single variable to find \( R \).

### Conclusion for Statement I:
Statement I alone does not provide enough information to determine Rahul's age because we cannot isolate Rahul's age without knowing either Arun's or Neeraj's age specifically.

### Step 2: Analyze Statement II
**Statement II:** Neeraj is 4 years older than Satish, and the ratio of the age of Satish to Rahul is 1:2.

1. Let the age of Satish be \( S \). Then Neeraj's age \( N \) can be expressed as:
\[ N = S + 4 \]

2. The ratio of Satish's age \( S \) to Rahul's age \( R \) is given as:
\[ \frac{S}{R} = \frac{1}{2} \implies R = 2S \]

3. Now we can express Neeraj's age in terms of Rahul's age:
\[ N = S + 4 = \frac{R}{2} + 4 \]

4. Substituting \( R = 2S \) into the equation gives us:
\[ N = S + 4 = S + 4 \]
This does not help us isolate \( R \) directly.

### Conclusion for Statement II:
Statement II alone also does not provide enough information to determine Rahul's age because we need to know either Satish's or Neeraj's age specifically.

### Final Conclusion:
Both statements I and II are not sufficient alone to determine Rahul's age after 2 years.

### Answer:
The answer is that neither statement alone is sufficient.