Question

The mean weight of $120$ students in the second year class of a college is $56kg$, If the mean weight of the boys and that of the girls in the class are $60kg$ and $50kg$ respectively, then the number of boys and girls separately in the class are

• A. $72,64$
• B. $38,64$
• C. $72,48$
• D. None of these

Answer 1

Answer: (C)

$72,48$

We know that the combined mean $A=\frac{n_1{A}_1+n_2{A}_2}{n_1+n_2}$ ...(1)
Here $A_1=$ mean weight of boys $=60kg$
$A_2=$ mean weight of girls $=50kg$
$A=$ combined mean $=56kg$
and $n_1+n_2=120$ ...(2)
So, from (1) and (2)
$56=\frac{n_1.60+n_2.50}{120}\Rightarrow 56\times 120=n_1.60+(120-n_1)50;\Rightarrow 120(56-50)=10n_1\Rightarrow n_1=72,n_2=48$
Thus, the number of boys $=72$ and the number of girls $=48$.