The average age of a man and son his son is 48 years. The ratio of their ages is 5:3 respectively. What is the son’s age?

Options

A. 36 years
B. 48 years
C. 60 years
D. 24 years

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the given information
We know that:
- The average age of a man and his son is 48 years.
- The ratio of their ages is 5:3.

### Step 2: Set up the equations
Let the age of the man be \(5x\) and the age of the son be \(3x\), where \(x\) is a common multiplier.

### Step 3: Write the equation for the average age
The average age of the man and his son can be expressed as:
\[ \text{Average Age} = \frac{\text{Age of Man} + \text{Age of Son}}{2} \]
Substituting the ages in terms of \(x\):
\[ 48 = \frac{5x + 3x}{2} \]

### Step 4: Simplify the equation
Combine the terms in the numerator:
\[ 48 = \frac{8x}{2} \]
This simplifies to:
\[ 48 = 4x \]

### Step 5: Solve for \(x\)
To find \(x\), we can rearrange the equation:
\[ x = \frac{48}{4} = 12 \]

### Step 6: Find the son's age
Now that we have \(x\), we can find the son's age:
\[ \text{Son's Age} = 3x = 3 \times 12 = 36 \text{ years} \]

### Conclusion
The son's age is **36 years**.

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