If the mean of the numbers 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

• A 75
• B 157
• C 82
• D 80

To solve the problem, we first need to find the value of \( x \) using the given mean of the first set of numbers.

Finding the Value of x

The numbers are: 27+x, 31+x, 89+x, 107+x, and 156+x. The mean is calculated as follows:

• Sum of the numbers: (27+x) + (31+x) + (89+x) + (107+x) + (156+x) = 410 + 5x
• Number of values: 5
• Mean formula: Mean = (Sum of values) / (Number of values)

Setting the mean equal to 82 gives us:

(410 + 5x) / 5 = 82

Solving for x

Multiplying both sides by 5:

410 + 5x = 410

5x = 410 - 410

5x = 0

x = 0

Calculating the New Mean

Now, we substitute \( x = 0 \) into the second set of numbers: 130+x, 126+x, 68+x, 50+x, and 1+x.

• New numbers: 130, 126, 68, 50, 1
• Sum of these numbers: 130 + 126 + 68 + 50 + 1 = 375
• Mean = 375 / 5 = 75

Final Answer

The mean of the second set of numbers is 75. Therefore, the correct answer is A 75.