I am three times as old as my son. 15 yr hence. I will be twice as old as my son. What is the sum of our present ages.

Answer

To solve the problem, we will follow these steps:

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

### Step 2: Set Up the First Equation
According to the problem, the father is three times as old as his son. This gives us our first equation:
\[ X = 3Y \quad \text{(1)} \]

### Step 3: Set Up the Second Equation
The problem states that 15 years from now, the father will be twice as old as his son. In 15 years, the father's age will be \( X + 15 \) and the son's age will be \( Y + 15 \). This gives us our second equation:
\[ X + 15 = 2(Y + 15) \quad \text{(2)} \]

### Step 4: Simplify the Second Equation
Now, we will simplify equation (2):
\[ X + 15 = 2Y + 30 \]
Rearranging gives:
\[ X - 2Y = 30 - 15 \]
\[ X - 2Y = 15 \quad \text{(3)} \]

### Step 5: Substitute Equation (1) into Equation (3)
Now we will substitute \( X \) from equation (1) into equation (3):
\[ 3Y - 2Y = 15 \]
This simplifies to:
\[ Y = 15 \]

### Step 6: Find the Father's Age
Now that we have the son's age, we can find the father's age using equation (1):
\[ X = 3Y = 3 \times 15 = 45 \]

### Step 7: Calculate the Sum of Their Present Ages
Now we can find the sum of their present ages:
\[ \text{Sum} = X + Y = 45 + 15 = 60 \]

### Final Answer
The sum of their present ages is \( 60 \) years.

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