The age of a man is three times the sum of the two sons . Five years hence , his ages will be double of the sum of the ages of his sons. The father's present age is:

Options

A. 40 years
B. 45 years
C. 50 years
D. 55 years

Answer

To solve the problem step by step, let's denote:

- The present age of the father as \( F \).
- The present ages of the two sons as \( S_1 \) and \( S_2 \).
- The sum of the ages of the two sons as \( S = S_1 + S_2 \).

### Step 1: Set up the equations based on the problem statement.

From the problem, we know:
1. The age of the father is three times the sum of the ages of his two sons.
\[ F = 3S \quad \text{(Equation 1)} \]

2. Five years hence, the father's age will be double the sum of the ages of his sons.
- In five years, the father's age will be \( F + 5 \).
- In five years, the ages of the sons will be \( S_1 + 5 \) and \( S_2 + 5 \), making the sum \( S + 10 \).
\[ F + 5 = 2(S + 10) \quad \text{(Equation 2)} \]

### Step 2: Substitute Equation 1 into Equation 2.

Substituting \( F \) from Equation 1 into Equation 2:
\[ 3S + 5 = 2(S + 10) \]

### Step 3: Simplify Equation 2.

Expanding the right side:
\[ 3S + 5 = 2S + 20 \]

### Step 4: Rearrange the equation to isolate \( S \).

Subtract \( 2S \) from both sides:
\[ 3S - 2S + 5 = 20 \]
\[ S + 5 = 20 \]

Now, subtract 5 from both sides:
\[ S = 15 \]

### Step 5: Substitute \( S \) back into Equation 1 to find \( F \).

Now that we have \( S \), substitute it back into Equation 1:
\[ F = 3S = 3 \times 15 = 45 \]

### Conclusion

The father's present age is \( 45 \) years.

---