The average score of boys in an examination of a school is 71 and that of girls is 73. The average score of school in that examination is 71.8. The ratio of the number of boys to the number of girls appeared in the examination, is 

Let there be $n_1$ boys and $n_2$ girls in the school. 

Let $\overline{X_1}$ and $\overline{X_2}$ be the average scores of boys and girls  respectively and $\overline{X}$ be the average of both boys and girls. Then, 

$\begin{array}{l}\overline{X_1}=71,\overline{X_2}=63,\overline{X}=71.8\\ \therefore \overline{X}=\frac{n_1\overline{X_1}+n_2\overline{X_2}}{n_1+n_2}\\ \Rightarrow 71.8=\frac{n_1\times 71+n_2\times 73}{n_1+n_2}\\ \Rightarrow 71.8\left(n_1+n_2\right)=71n_1+73n_2\\ \Rightarrow 71.8n_1+71.8n_2=71n_1+73n_2\\ \Rightarrow 0.8n_1=1.2n_2\\ \Rightarrow 8n_1=12n_2\Rightarrow \frac{n_1}{n_2}=\frac{12}{8}=\frac{3}{2}\end{array}$

Hence, $n_1:n_2=3:2$