Question

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

Answer 1

Given:

N_b + N_g = 150 (Equation-1)

$$\begin{gathered} {\overline{\mathrm{X}}}_{b,g}=60kg \\ {\overline{\mathrm{X}}}_b=70kg \\ {\overline{\mathrm{X}}}_g=55kg \end{gathered}$$

N_g = 150 − N_b (From eqn-1)

_{We know,}
$$\begin{gathered} CombinedMean\left({\overline{X}}_{b,g}\right)=\frac{N_b\times {\overline{X}}_b+N_g\times {\overline{X}}_g}{N_b+N_g} \\ or,60=\frac{70N_b+55\left(150-N_b\right)}{150} \\ 9000=70N_b-55N_b+8250 \\ 15N_b=750 \\ {\mathit{N}}_{\mathbf{b}}=50 \\ {\mathit{N}}_{\mathbf{g}}=150-N_b=150-50=100 \end{gathered}$$

Therefore,

No. of boys = N_b = 50
No. of Girls = N_g = 100