Question

There are 36 members in a student council in a school and the ratio of the number of boys to the number of girls is 3 : 1. How many more girls should be added to the council so that the ratio of number of boys to the number of girls may be 9 :5 ?

Answer 1

Total numbers of boys in student council = $\frac{3}{3+1}\times 36$
= $\frac{3}{4}\times 36$
= 27 boys

And

Total numbers of girls in student council = $\frac{1}{3+1}\times 36$
= $\frac{1}{4}\times 36$
= 9 Girls

Let x girls be added to get the required ratio ( 9 : 5 ) ,
Than we have
$\frac{27}{9+x}=\frac{9}{5}$
By invertendo we have
$\frac{9+x}{27}=\frac{5}{9}$
$\frac{9+x}{3}=\frac{5}{1}$
or $9+x=3\times 5$
or $9+x=15$

or x= 15-9

$\therefore x=6$

So,

6 girls need to be added to get our ratio as 9 : 5.