In a class of $80$ students, $40\%$ are boys and the rest are girls. The average score in mathematics of all the students is $72$. If the average score of the girls is $66$, then what is the average score of the boys?

Let's find the number of boys and girls first. Total students = $80$ Percentage of boys = $40\%$ Number of boys = $40\%\text{ of }80=32$ Number of girls = $80-32=48$ The ratio of the number of boys to girls is:
$$\text{Ratio}=\frac{32}{48}=\frac{2}{3}$$
Let the average score of boys be $x$.Given:Average score of girls = $66$ Combined average score of all students = $72$ Using the weighted average formula:
$$\text{Combined Average}=\frac{(\text{Number of boys}\times x)+(\text{Number of girls}\times 66)}{\text{Total students}}$$
Alternatively, using the simplified ratio ($2:3$):
$$72=\frac{2x+3(66)}{2+3}$$
$$72=\frac{2x+198}{5}$$
$$72\times 5=2x+198$$
$$360=2x+198$$
$$2x=360-198$$
$$2x=162$$
$$x=81$$
Thus, the average score of the boys is $81$.