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# 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}} \\$

Answer Verified
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:
Add up all the numbers,
Then divide by how many numbers there are.
Given, ${\text{82 = }}\dfrac{{27 + x + 31 + x + 89 + x + 107 + x + 156 + x}}{5}$
$\Rightarrow 82 \times 5 = 410 + 5x \\ \therefore x = 0 \\$
Therefore, required mean is
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.

Note: - Whenever we face such a type of question when the mean is given, always try to find the average to get the value of unknown terms and then put the value of that term to get the answer.
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