Question

The number of boys and girls in a class is in the ratio 8 : 5. The number of boys is 9 more than the number of girls. The total number of students in the class is​

Answer 1

let number of boys be y

let number of girls be x

so ,

y = x + 9 __(1)

given ratio 8 : 5

$\frac{8}{5} = \frac{y}{x} = \frac{x + 9}{x} \\ \\ 8x = 5x + 45 \\ \\ 8x - 5x =3x = 45 \\ \\ x = 15$

so ,

• number of girls = 15 girls
• number of boys = 15 + 9 = 24 boys

total students = 24 + 15 = 39 students

Answer 2

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

Let

Number of boys=8x

Number of girls=5x

ATQ

$\begin{gathered}\\ \sf\longmapsto 8x=5x+9\end{gathered}$

take 5x to left side

$\begin{gathered}\\ \sf\longmapsto 8x-5x=9\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto 3x=9\end{gathered}$

Take 3 to right side

$\begin{gathered}\\ \sf\longmapsto x=\dfrac{9}{3}\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto x=3\end{gathered}$

Now

$\begin{gathered}\\ \sf\longmapsto Number\:of\:Boys=8x=8(3)=24\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto Number\:of\:Girls=5x=5(3)=15\end{gathered}$

$\sf{\underline{\overline{\pink{Strength \:of\: class\::-}}}}$

$\begin{gathered}\\ \sf\longmapsto Number\:of\:boys+Number\:of\:Girls\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto 24+15\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto 39\end{gathered}$

There are total 39 students in class.