Question

A school has 630 students. The ratio of the number of boys to the number of girls is 3:2. The ratio changes to 7:5 after the admission of 90 new students. Find the number of newly admitted boys.

Answer 1

Let the number of boys be $3x$

Then the number of girls $=2x$

$\therefore 3x+2x=630$

$\Rightarrow 5x=630\therefore x=126$

$\Rightarrow$ number of boys $=3x=3\times 126=378$

And number of girls $=2x=2\times 126=252$

After admission of $90$ students we have total number of students $=630+90=720$

Now, let the number of boys be $7x$

Then, the number of girls $=5x$

$\therefore 7x+5x=720$

$\Rightarrow 12x=720$

$\therefore x=60$

$\Rightarrow$ number of boys $=7x=7\times 60=420$

And number of girls $=5x=5\times 60=300$

$\therefore$ Number of newly admitted boys $=420-378=42$