If 6 years are subtracted from the present age of Panas and take 25% of that then we get the present age of his only son. 4 years ago, his daughter's age is 7 years more than his son. Sum of daughter's present age and his wife's present age is 10 years more than Panas's present age , then find the present age of Panas if average of present age of entire family is 30.25 years ?

Options

A. 45 year
B. 50 year
C. 60 year
D. 40 year

Explanation

To solve the problem step by step, let's denote the present age of Panas as \( x \).

### Step 1: Determine the son's age
According to the problem, if 6 years are subtracted from Panas's age and then 25% of that is taken, we get the present age of his son.

So, the son's age can be expressed as:
\[ \text{Son's age} = \frac{x - 6}{4} \]

### Step 2: Determine the daughter's age
It is given that 4 years ago, the daughter's age was 7 years more than the son's age.

Let’s denote the present age of the son as \( S \):
\[ S = \frac{x - 6}{4} \]
4 years ago, the son's age was:
\[ S - 4 = \frac{x - 6}{4} - 4 \]
4 years ago, the daughter's age was:
\[ D - 4 = S - 4 + 7 \]
Thus, the present age of the daughter \( D \) can be expressed as:
\[ D = \left(\frac{x - 6}{4} - 4 + 7\right) + 4 = \frac{x - 6}{4} + 3 \]

### Step 3: Determine the wife's age
The problem states that the sum of the daughter's present age and the wife's present age is 10 years more than Panas's present age.

Let’s denote the present age of the wife as \( W \):
\[ D + W = x + 10 \]
Substituting \( D \) from the previous step:
\[ \left(\frac{x - 6}{4} + 3\right) + W = x + 10 \]
From this, we can express \( W \):
\[ W = x + 10 - \left(\frac{x - 6}{4} + 3\right) \]
Simplifying this:
\[ W = x + 10 - \frac{x - 6}{4} - 3 \]
\[ W = x + 7 - \frac{x - 6}{4} \]
To combine terms, we can express \( x \) as \( \frac{4x}{4} \):
\[ W = \frac{4x}{4} + \frac{28}{4} - \frac{x - 6}{4} \]
\[ W = \frac{4x + 28 - x + 6}{4} = \frac{3x + 34}{4} \]

### Step 4: Set up the average age equation
The average age of the family is given as 30.25 years. The family consists of Panas, his son, his daughter, and his wife (4 members). The average age can be expressed as:
\[ \text{Average} = \frac{x + \frac{x - 6}{4} + \left(\frac{x - 6}{4} + 3\right) + \frac{3x + 34}{4}}{4} = 30.25 \]
Multiplying both sides by 4:
\[ x + \frac{x - 6}{4} + \left(\frac{x - 6}{4} + 3\right) + \frac{3x + 34}{4} = 121 \]

### Step 5: Combine and simplify the equation
Combining all terms:
\[ x + \frac{x - 6 + x - 6 + 12 + 3x + 34}{4} = 121 \]
\[ x + \frac{5x + 34}{4} = 121 \]
Multiply through by 4 to eliminate the fraction:
\[ 4x + 5x + 34 = 484 \]
\[ 9x + 34 = 484 \]
Subtract 34 from both sides:
\[ 9x = 450 \]
Divide by 9:
\[ x = 50 \]

### Conclusion
The present age of Panas is \( \boxed{50} \).