Question

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

• A. $3:2$
• B. $3:4$
• C. $1:2$
• D. $2:1$

Answer 1

The correct option is A $3:2$

Let there be $n_1$ boys and $n_2$ girls.
and $\overline{X_1}$ and $\overline{X_2}$ be the average scores of boys and girls respectively.
Then $\overline{X_1}=71,\overline{X_2}=63$ and $\overline{X}=71.8$
$\therefore \overline{X}=\frac{n_1\overline{X_1}+n_2\overline{X_2}}{n_1+n_2}$
$\Rightarrow 71.8=\frac{n_1\times 71+n_2\times 73}{n_1+n_2}$
$\Rightarrow 71.8n_1+71.8n_2=71n_1+73n_2$
$\Rightarrow 0.8n_1=1.2n_2\Rightarrow 8n_1=12n_2$
$\Rightarrow \frac{n_1}{n_2}=\frac{12}{8}=\frac{3}{2}$