Question

The average age of three boys is $15years$ and their ages are in proportion$3:5:7$. What is the age in years of the youngest boy?

Answer 1

Given proportion is$3:5:7$

Let the age of three boys be $3x,5x$and $7x.$

According to given question,

Average age$=15years$

We know that,

$Averageage=\frac{sumofagesofallpersons}{totalnumberofpersons}$

$$\begin{gathered} \Rightarrow 15=\frac{\left(3x+5x+7x\right)}{3} \\ \Rightarrow 15\times 3=15x \\ \Rightarrow 45=15x \\ \Rightarrow x=\frac{45}{15}=3 \end{gathered}$$

Thus,

Ages of boys are,

$$\begin{gathered} 3x=3\times 3=9years \\ 5x=5\times 3=15years \\ 7x=7\times 3=21years \end{gathered}$$

Hence, the age of youngest boy is$9years$