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

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157

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Solution

The correct option is A 75
$Given,$
$82 = \frac{(27 + x) + (31 + x) + (89 + x) + (107 + x) + (156 + x)}{5}$
$\Rightarrow 82 \times 5 = 410 + 5 x \Rightarrow 410 - 410 = 5 x \Rightarrow x = 0$
$∴ Required mean is,$
$¯ ¯ ¯ x = \frac{130 + x + 126 + x + 68 + x + 50 + x + 1 + x}{5}$
$¯ ¯ ¯ x = \frac{375 + 5 x}{5} = \frac{375 + 0}{5} = \frac{375}{5} = 75.$

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