Question

If the mean of the number $27+x,31+x,89+x,107+x,156+x$ is $82,$ then the mean of $130+x,126+x,68+x,50+x,1+x$ is ___.

Answer 1

$Given,$
$82=\frac{(27+x)+(31+x)+(89+x)+(107+x)+(156+x)}{5}$
$\Rightarrow 82\times 5=410+5x\Rightarrow 410-410=5x\Rightarrow x=0$
$\therefore Requiredmeanis,$
$\overline{x}=\frac{130+x+126+x+68+x+50+x+1+x}{5}$
$\overline{x}=\frac{375+5x}{5}=\frac{375+0}{5}=\frac{375}{5}=75$