Question

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

• A. $100,50$
• B. $50,100$
• C. $75,75$
• D. $60,90$

Answer 1

The correct option is B

$50,100$

The explanation for the correct option:

Given that total student in the class is $150$ and the mean weight is $60\mathrm{kg}$.

$\therefore \mathrm{Total}\mathrm{weight}=150\times 60=9000\mathrm{kg}$

Let us consider the total number of boys be $x$ and given that the mean weight of boys is$70\mathrm{kg}$.

$\therefore \mathrm{Total}\mathrm{weight}\mathrm{of}\mathrm{boys}=70\times x=70x\mathrm{kg}$

$\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{girls}=\mathrm{Total}\mathrm{students}-\mathrm{number}\mathrm{of}\mathrm{boys}=150-x$

Since the mean weight of girls is $55\mathrm{kg}$.

$$\begin{gathered} \therefore \mathrm{Total}\mathrm{weight}\mathrm{of}\mathrm{girls}=55\times (150–x) \\ \Rightarrow =(55\times 150)-55x \\ \Rightarrow =(8250-55x)\mathrm{kg} \end{gathered}$$

$$\begin{gathered} \because \mathrm{Total}\mathrm{weight}=\mathrm{weight}\mathrm{of}\mathrm{boys}+\mathrm{weight}\mathrm{of}\mathrm{girls} \\ \therefore 9000=70x+(8250-55x) \\ \Rightarrow 9000=70x+8250-55x \\ \Rightarrow 9000-8250=70x–55x \\ \Rightarrow 750=15x \\ \Rightarrow x=\frac{750}{15} \\ \Rightarrow x=50 \end{gathered}$$

So, the number of boys $=50$

$\therefore \mathrm{Number}\mathrm{of}\mathrm{girls}=150-50=100$

Hence, the correct option is $B$.