The ratio of the ages of A and B is 3:8, if B's age is 24 years, then find the age of A.

Explanation

To solve the problem step-by-step, we will follow the given information and use the concept of ratios.

### Step 1: Understand the Ratio
The ratio of the ages of A and B is given as 3:8. This means that for every 3 parts of A's age, B has 8 parts.

### Step 2: Set Up the Ratio
Let the age of A be represented as \( A \) and the age of B as \( B \). According to the ratio:
\[ \frac{A}{B} = \frac{3}{8} \]

### Step 3: Substitute the Known Value
We know that B's age is 24 years. So, we can substitute \( B \) in the ratio:
\[ \frac{A}{24} = \frac{3}{8} \]

### Step 4: Cross Multiply
To find the value of A, we will cross multiply:
\[ A \cdot 8 = 3 \cdot 24 \]

### Step 5: Calculate the Right Side
Now, calculate \( 3 \cdot 24 \):
\[ 3 \cdot 24 = 72 \]
So, we have:
\[ 8A = 72 \]

### Step 6: Solve for A
Now, divide both sides by 8 to find A:
\[ A = \frac{72}{8} = 9 \]

### Conclusion
Therefore, the age of A is 9 years.

---