The average age of three boys is 15yr . If the ratio of their ages is 3:5:7 , what is the age of the oldest boy ?

Options

A. 7yr
B. 14yr
C. 20yr
D. 21yr

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript:

### Step-by-Step Solution:

1. **Understanding the Average Age**:
The average age of the three boys is given as 15 years.

2. **Using the Ratio of Ages**:
The ratio of their ages is given as 3:5:7. We can represent their ages in terms of a variable \( x \):
- Age of the first boy = \( 3x \)
- Age of the second boy = \( 5x \)
- Age of the third boy = \( 7x \)

3. **Setting Up the Equation for Average**:
The formula for average is:
\[ \text{Average} = \frac{\text{Sum of ages}}{\text{Number of boys}} \]
Here, the sum of ages is \( 3x + 5x + 7x \) and the number of boys is 3. Therefore, we can write:
\[ 15 = \frac{3x + 5x + 7x}{3} \]

4. **Simplifying the Equation**:
Combine the terms in the numerator:
\[ 15 = \frac{15x}{3} \]
Now, simplify the right side:
\[ 15 = 5x \]

5. **Solving for \( x \)**:
To find \( x \), multiply both sides by 3:
\[ 15 \times 3 = 5x \implies 45 = 5x \]
Now, divide both sides by 5:
\[ x = \frac{45}{5} = 9 \]

6. **Finding the Ages of Each Boy**:
Now that we have \( x = 9 \), we can find the ages:
- Age of the first boy = \( 3x = 3 \times 9 = 27 \) years
- Age of the second boy = \( 5x = 5 \times 9 = 45 \) years
- Age of the third boy = \( 7x = 7 \times 9 = 63 \) years

7. **Identifying the Oldest Boy**:
The oldest boy is the one with the highest age, which is \( 63 \) years.

### Final Answer:
The age of the oldest boy is **63 years**.