The sum of the ages of a son and father is 56 years. After four years, the age of the father will be three times that of the son. Their present ages respectively are-

Options

A. 12 years, 44years
B. 16 years,42 years
C. 16 years,48years
D. 18 years, 36 years

Answer

To solve the problem, we will use algebra to find the present ages of the son and the father.

### Step 1: Define Variables
Let the present age of the son be \( S \) years and the present age of the father be \( F \) years.

### Step 2: Set Up the Equations
From the problem, we have two pieces of information:
1. The sum of their ages is 56 years:
\[ S + F = 56 \quad \text{(Equation 1)} \]
2. After 4 years, the father's age will be three times the son's age:
\[ F + 4 = 3(S + 4) \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
Let's simplify Equation 2:
\[ F + 4 = 3(S + 4) \]
Expanding the right side:
\[ F + 4 = 3S + 12 \]
Now, rearranging gives:
\[ F = 3S + 12 - 4 \]
\[ F = 3S + 8 \quad \text{(Equation 3)} \]

### Step 4: Substitute Equation 3 into Equation 1
Now we will substitute Equation 3 into Equation 1:
\[ S + (3S + 8) = 56 \]
Combining like terms:
\[ 4S + 8 = 56 \]
Subtracting 8 from both sides:
\[ 4S = 48 \]
Dividing by 4:
\[ S = 12 \]

### Step 5: Find the Father's Age
Now that we have the son's age, we can find the father's age using Equation 1:
\[ F = 56 - S \]
Substituting \( S = 12 \):
\[ F = 56 - 12 = 44 \]

### Conclusion
The present ages of the son and father are:
- Son's age: 12 years
- Father's age: 44 years

### Summary of the Solution
- Present age of the son: 12 years
- Present age of the father: 44 years