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.

Let the number of boys and girls in the class be $n_1$ and $n_2$respectively. Then, 

$n_1+n_2=150$                            …(i)

We have,

$\overline{X_1}=$Mean weight of boys $=70\mathrm{kg}$$\Rightarrow 10n_1=5n_2\Rightarrow 2n_1=n_2$

$\overline{X_2}=$ Mean weight of girls $=55 kg$

$\overline{X}=$ Mean weight of all student $=60 kg.$

$\begin{array}{l}\therefore \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\overline{X}=\frac{n_1\overline{X_1}+n_2\overline{X_2}}{n_1+n_2}\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}60=\frac{n_1\times 70+n_2\times 55}{n_1+n_2}\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}60\left(n_1+n_2\right)=70n_1+55n_2\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}60n_1+60n_2=70n_1+55n_2\end{array}$

$\Rightarrow 10n_1=5n_2\Rightarrow 2n_1=n_2$  …(ii)

From (i) and (ii), we have $n_1$ = 100, $n_2$ = 50

Hence, there are 50 boys and 100 girls in the class.