Question

The average age of the group having $3$ members is $84$. One more person joins the group and now the average becomes $80$. Now a fifth person comes whose age is $3$ years more than that of fourth person replaces the first person. After this the average age of the group becomes $79$. What is the age of the first person?

Answer 1

Let the ages of five persons be $A,B,C,D$ and $E$.

$\Rightarrow$ Total age of $A,B$ and $C=84\times 3=252$

$\Rightarrow$ Total age of $A,B,C$ and $D=80\times 4=320$

$\Rightarrow$ Age of $D=320-252=68$

$\therefore$ Age of $E=68+3=71$

$\Rightarrow$ Total age of $B,C,D$ and $E=79\times 4=316$

$\Rightarrow$ $(A+B+C+D)-(B+C+D+E)=320-316$

$\therefore$ $A-E=4$

$\Rightarrow$ $A-71=4$ [ $E=71$ ]

$\therefore$ $A=75$