If the age of Rahul is 5 years more than his friend Ajay's age and the age of Rahul's wife is 6 years less than Rahul, and Ajay's wife is 1 year older than Rahul's wife, then which of the following statements is true?

Options

A. Rahul's age and Ajay's wife's age are same.
B. Ajay's wife's age and Ajay's age are same.
C. Rahul and Ajay are of the same age.
D. Rahul's and Ajay's ages difference is 3 years.

Explanation

To solve the problem step by step, we will define the ages of Rahul, Ajay, and their wives based on the information provided.

### Step 1: Define Variables
Let:
- \( A \) = Age of Ajay
- \( R \) = Age of Rahul
- \( R_w \) = Age of Rahul's wife
- \( A_w \) = Age of Ajay's wife

### Step 2: Set Up Equations Based on Given Information
From the problem statement, we have the following relationships:
1. Rahul's age is 5 years more than Ajay's age:
\[ R = A + 5 \]
2. Rahul's wife is 6 years younger than Rahul:
\[ R_w = R - 6 \]
3. Ajay's wife is 1 year older than Rahul's wife:
\[ A_w = R_w + 1 \]

### Step 3: Substitute Rahul's Age into the Wife's Age Equation
Substituting the expression for \( R \) into the equation for \( R_w \):
\[ R_w = (A + 5) - 6 = A - 1 \]

### Step 4: Substitute into Ajay's Wife's Age Equation
Now we can substitute \( R_w \) into the equation for \( A_w \):
\[ A_w = (A - 1) + 1 = A \]

### Step 5: Analyze the Results
From the equations, we find:
- Ajay's age \( A \) is equal to Ajay's wife's age \( A_w \).
- Rahul's age \( R \) is 5 years older than Ajay's age.

### Conclusion
Thus, we can conclude:
- Ajay's age and Ajay's wife's age are the same.

### Final Answer
The correct statement is that Ajay's age and Ajay's wife's age are the same.