Question

The mean of a group of eleven consecutive natural numbers is $m$. What will be the percentage change in the mean when next six consecutive natural numbers are included in the group?

• A. $m$%
• B. $\frac{m}{3}$%
• C. $\frac{m}{300}$%
• D. $\frac{300}{m}$%

Answer 1

The correct option is D $\frac{300}{m}$%

$\frac{\left(x\right)+(x+1)+(x+2)+.....+(x+10)}{11}=m$
$\Rightarrow 11x+\frac{10\left(11\right)}{2}=11m$
$\Rightarrow x+5=m.....\left(1\right)$
Now, $\frac{\left(x\right)+(x+1)+(x+2)+...+(x+16)}{17}$
$=\frac{17x+\frac{16\left(17\right)}{2}}{17}=x+8$
$=(m-5)+8$
$=m+3$
% change in mean $=\frac{(m+3)-m}{m}\times 100$
$=\left(\frac{300}{m}\right)$%.