Question

# If the mean of number ${\text{ }}27 + x,{\text{ }}31 + x,{\text{ }}107 + x,{\text{ }}156 + x$is${\text{82}}$, then the mean of $130 + x,{\text{ 126}} + x,{\text{ 68}} + x,{\text{ 50}} + x,{\text{ 1}} + x{\text{ is}}$${\text{A}}{\text{. 79}} \\ {\text{B}}{\text{. 157}} \\ {\text{C}}{\text{. 82}} \\ {\text{D}}{\text{. 75}} \\$

Hint: - Here, we calculate the average of numbers to find unknown values. Average is the sum of all numbers divided by the total number of values.

Mean is the average of the numbers: a calculated central value of a set of numbers.
To calculate it:
Given, ${\text{82 = }}\dfrac{{27 + x + 31 + x + 89 + x + 107 + x + 156 + x}}{5}$
$\Rightarrow 82 \times 5 = 410 + 5x \\ \therefore x = 0 \\$
Mean${\text{ = }}\dfrac{{130 + x + 126 + x + 68 + x + 50 + x + 1 + x}}{5}$
${\text{ = }}\dfrac{{375 + 5x}}{5} = \dfrac{{375 + 0}}{5} = 75$
$\therefore$Option D is the correct answer.