Question

After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member?

• A. $2$ years
• B. $4$ years
• C. $8$ years
• D. $15$ years

Answer 1

The correct option is D $15$ years

Let the five members ages be $x_1,x_2,x_3,x_4,x_5$

Let the one of the old member age be $x_1$

Let the new member age be $x_6$

Given that after replacing an old member by the new member, the average age of five members is the same as it was 3 years ago

Therefore, $\frac{(x_1-3)+(x_2-3)+(x_3-3)+(x_4-3)+(x_5-3)}{5}=\frac{x_2+x_3+x_4+x_5+x_6}{5}$

$⟹x_1+x_2+x_3+x_4+x_5-3\left(5\right)=x_2+x_3+x_4+x_5+x_6$

$⟹x_1-15=x_6$

$⟹x_1-x_6=15$

Therefore the difference between the ages of the replaced and the new member is $15$ years