Question

In a cricket league match, there are both male and female members. If $m$ is the average age of male members and $f$ is the average age of female members, $a$ is the total average age and $65$ percent of the league's members are male, then which one of the following statements relate about $m$, $f$ and $a$?

• A. If $m<f$, then $a>\frac{m+f}{2}$
• B. If $m>f$, then $a<\frac{m+f}{2}$
• C. If $m<f$, then $a<\frac{m+f}{2}$
• D. $a=\frac{m+f}{2}$

Answer 1

The correct option is C If $m<f$, then $a<\frac{m+f}{2}$

Suppose total members$=100$

Age total of males $=m\times 65$

Age total of females $=f\times 35$

$a=\frac{m\times 65+f\times 35}{100}$

now, try writing $a$ with $\frac{(m+f)}{2}$ in the expression to compare.

$a=\frac{(m+f)}{2}+\frac{3}{20}(m-f)$

So, if $m>f$, $a>\frac{(m+f)}{2}$

else, if $m<f$, $a<\frac{(m+f)}{2}$