Question

The mean age of a group of persons is $72$ years and another group of persons is $63$ years. If the mean age of all the persons of these two groups is $70,$ then the ratio of number of persons in the two groups is

• A. $\frac{3}{4}$
• B. $\frac{5}{2}$
• C. $\frac{7}{2}$
• D. $\frac{8}{7}$

Answer 1

The correct option is C $\frac{7}{2}$

$\text{Let number of person in the first group}=n_1$
and Mean $X_1=72$
$\text{and number of person in the second group}=n_2$
Mean $X_2=63$

$\text{Total number of persons in total}=n_1+n_2$
Let $X$ be the average mean.
Then $X=\frac{72\times n_1+63\times n_2}{n_1+n_2}=70$
$\Rightarrow 70n_1+70n_2=72n_1+63n_2$
$\Rightarrow \frac{n_1}{n_2}=\frac{7}{2}$