The ratio of the number of boys to the number of girls in a school of 560 pupils is 5 : 3. If 10 new boys are admitted, find how many new girls may be admitted so that the ratio of number of boys to the number of girls may change to 3 : 2.

Total students = 560

Ratio of the number of boys to the number of girls = 5 : 3.

Sum of ratio = 5 + 3 = 8.

Number of boys = $\dfrac{5}{8}$ x 560 = 5 x 70 = 350.

Number of girls = $\dfrac{3}{8}$ x 560 = 210.

10 new boys are admitted in school , so total boys now = 350 + 10 = 360.

Let new girls to be admitted be x, so now total girls = (210 + x)

New boys to girls ratio = 3 : 2

$\therefore 360 : (210 + x) = 3 : 2 \\[0.5em] \Rightarrow \dfrac{360}{210 + x} = \dfrac{3}{2} \\[0.5em] \Rightarrow 720 = 3(210 + x) \\[0.5em] \Rightarrow 3x + 630 = 720 \\[0.5em] \Rightarrow 3x = 720 - 630 \\[0.5em] \Rightarrow 3x = 90 \\[0.5em] \Rightarrow x = 30.$

Hence, the number of new girls to be admitted are 30.