Question

The ratio of the number of boys to the number of girls in a school of $672$ students is $5:7.$ When some new boys and girls are admitted, the number of girls increases by $8$ and the ratio of boys to girls changes to $3:4$. Calculate the number of new boys admitted.

Answer 1

As the ratio of boys to girls is $5:7$ and the total number of students is $672$,
Number of boys $=\frac{5}{5+7}\times 672=280$
And Number of girls $=\frac{7}{5+7}\times 672=392$
Let the number of boys admitted be $a$. Then total number of boys $=280+a$
As the number of girls increases by $8$. total number of girls $392+8=400$
Given, new ratio of boys to girls is $3:4$
$=>280+a:400=3:4$

$=>\frac{280+a}{400}=\frac{3}{4}$

On cross multiplying,
$280+a=\frac{3}{4}\times 400$
$280+a=300$
$=>a=20$
So, the number of new boys admitted is $20$.