Question

15. The number of girls varied directly as the number of boys and inversely as the number of teachers. When there were 50 girls, there were 20 teachers and 10 boys. How many boys were there when there were 10 girls and 100 teachers?

Answer 1

Answer:

Number of boys were $10.$

Step-by-step explanation:

According to Direct proportion:

When $x$ varies directly with $y$ then $x=ky$, {where $k$ is proportionality                            

                                                                                             constant}.

Let number of girl be $g$,

Number of boy be $b$,

And number of teacher be $t$.

From the question,

Number of girls varies directly as the number of boys and inversely with number of teacher.

So, Using direct proportion we get an equation

                        $g=\frac{k\times b}{t}$                    ........(a)

Case 1: $g=50$ ,  $t=20$ ,   and $b=10$

Now,  substituting all the values in equation (a) we get,

             $50=\frac{k\times 10}{20}$  ⇒ $k\times 10=50\times20$

                                          $k=100$

Case 2: $g=10$ ,  $t=100$ , $b=?$

Finding the number of boys using  $k=100$ we get,

            $10=\frac{100\times b}{100}$     ⇒ $b=10$

Therefore, Number of boys were $10.$