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

Ratio of boys to girls = 3 : 2.

No. of boys = $\dfrac{3}{3 + 2} \times 630 = \dfrac{3}{5} \times 630 = 378.$

No. of girls = $\dfrac{2}{3 + 2} \times 630 = \dfrac{2}{5} \times 630 = 252.$

Let no. of newly admitted boys be x and so girls = 90 - x.

According to question on admission of 90 new students ratio changes to 7 : 5.

$\therefore \dfrac{378 + x}{252 + 90 - x} = \dfrac{7}{5} \\[1em] \Rightarrow \dfrac{378 + x}{342 - x} = \dfrac{7}{5} \\[1em] \Rightarrow 5(378 + x) = 7(342 - x) \\[1em] \Rightarrow 5(378 + x) = 7(342 - x) \\[1em] \Rightarrow 1890 + 5x = 2394 - 7x \\[1em] \Rightarrow 5x + 7x = 2394 - 1890 \\[1em] \Rightarrow 12x = 504 \\[1em] \Rightarrow x = \dfrac{504}{12} \\[1em] \Rightarrow x = 42.$

Hence, there are 42 newly admitted boys.