Question

The average age of a group of eight is same as it was $3$ years ago. When a young member is substituted for an old member, the incoming member is younger to the outgoing member by:

• A. $11$ years
• B. $24$ years
• C. $28$ years
• D. $16$ years

Answer 1

The correct option is B $24$ years

let presently the member be $x_1,x_2,x_3...........x_8$

So the average age$=\frac{x_1+x_2+x_3+.......+x_8}{8}$......1

Now the average age of all the members 3 years ago$=\frac{x_1+x_2+x_3+......+x_8-8\times 3}{8}$

$\Rightarrow \frac{x_1+x_2+x_3+.....x_8-24}{8}$

if $x_1$ the younger member is replaced by the older member$y_1$then$=\frac{y_1+x_2+x_3+.......x_8-24}{8}$........2

By equation 1 and 2 we get

$\frac{x_1+x_2+x_3+.....+x_8}{8}=\frac{y_1+x_2+x_3+.....+x_8-24}{8}$

$\Rightarrow x_1=y_1+24$

$\Rightarrow x_1-y_1=24$