The ratio of the number of girls to the number of boys in a school of 720 students is 3:5.If 18 new boys are admitted in the school,find how many girls may be admitted so that the ratio of the number of girls to the number of boys may change to 2:3.

The ratio of number of girls to the number of boys is 3:5
Sum of the terms of the ratio=3+5=8
$\therefore$ The number of girls in the school=$\frac{3}{8}\times720$=$270$ and,
The number of boys in the school=$\frac{5}{8}\times720$=$450$

Let the number of new girls admitted be x,then the number of girls become (270+x).
After admitting 18 new boys,the number of boys become 450+18 i.e., 468
According to the given,
$\frac{270+x}{468}=\frac{2}{3}$
$\Rightarrow 3(270+x)=2\times468$
$\Rightarrow 810+3x=936$
$\Rightarrow 3x=936-810$
$\Rightarrow 3x=126$
$\Rightarrow x=\frac{126}{3}=42$
Hence the number of new girls admitted is 42

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