Question

The mean weight of $150$ students in a certain class is $60$ kg. The mean weight of boys in the class is $70$ kg and that of girls is $55$ kg. The number of boys and the number of girls in the class are respectively

• A. $100$ and $50$
• B. $50$ and $100$
• C. $150$ and $100$
• D. $100$ and $150$

Answer 1

The correct option is B $50$ and $100$

Let the number of boys and girls in the class be $n_1$ and $n_2$ respectively. Then
$n_1+n_2=150$
We have
$\overline{X_1}$ = Mean weight of boys = $70$ kg
$\overline{X_2}$ = Mean weight of girls = $55$ kg
$\overline{X}$ = Mean weight of all the students = $60$ kg
$\therefore \overline{X}=\frac{n_1\overline{X_1}+n_2\overline{X_2}}{n_1+n_2}$
$\Rightarrow 60=\frac{n_1\times 70+n_2\times 55}{n_1+n_2}$
$\Rightarrow 60n_1+60n_2=70n_1+55n_2$
$\Rightarrow 10n_1=5n_2\Rightarrow 2n_1=n_2$
Hence there are $50$ boys and $100$ girls