Question

The average age of a class is $15.8$ years. The average age of the boys in the class Is $16.4$ years while that of the girls is $15.4$ years. What is the ratio of boys to girls in the class?

Answer 1

Let the number of boys in the class be $x$

Let the number of girls in the class be $y$

So, the total number of students$=x+y$

We know that,

$Average=\frac{sumofagesofallstudents}{numberofstudents}$

$\Rightarrow 15.8=\frac{sumofagesofallstudents}{\left(x+y\right)}$

Sum of ages of the class$=15.8\times (x+y)$

$=15.8x+15.8y......\left(1\right)$

We have also,

Average of boys ages$=16.4years$

So, Total age of the boys $=16.4xyears$

Average of girls ages$=15.4years$

So, Total age of girls $=15.4yyears$

Thus, we have the total ages of girls and boys $=16.4x+15.4y........\left(2\right)$

Now, from $\left(1\right)$ and $\left(2\right)$

$\begin{array}{rcl}& \Rightarrow & 16.4x+15.4y=15.8x+15.8y\\ & \Rightarrow & 16.4x-15.8x=15.8y-15.4\\ & \Rightarrow & 0.6x=0.4y\\ & \Rightarrow & \frac{x}{y}=\frac{0.4}{0.6}\\ & =& \frac{2}{3}\end{array}$

Thus, $x:y=2:3$

Therefore, the ratio of boys to girls in the class is $2:3$