Let’s denote the ages of the three boys as 3x, 5x, and 7x, where x is a common factor. The ratio of their ages is given as 3:5:7.

The average age of the three boys is given as 15 years. The average is calculated by adding up the ages and dividing by the number of boys.

$\text{Average}=\frac{\text{SumofAges}}{\text{NumberofBoys}}$

In this case, the sum of their ages is

$3x+5x+7x=15x$ and there are three boys.

$15=\frac{15x}{3}$

Now, solving for x:

$15=5x$

$x=3$Now that we have the value of x, we can find the ages of the three boys:

Age of the youngest boy:

$3x=3\times 3=9$years.

Therefore, the age of the youngest boy is 9 years.