If the mean of the number 27+x,31+x,89+x,107+x,156+x is 82, then the mean of 130

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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

Options:

A . 75

B . 157

C . 82

D . 80

Answer: Option A
:
A

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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