Question

When 8 is added to each of the given 'n' numbers, the sum of the resulting numbers is 207. When 5 is subtracted from each of the given 'n' numbers, the sum of the resulting numbers is 77. What is the mean of the given 'n' numbers?

• A. 10.6
• B. 11.8
• C. 12.7
• D. 13.4

Hint:

For problems involving the sum of numbers with added or subtracted constants, set up equations and solve for \(S\) and \(n\).

Answer 1

The Correct Option is B

Let the sum of the given 'n' numbers be \(S\). - When 8 is added to each number, the sum becomes \(S + 8n = 207\). - When 5 is subtracted from each number, the sum becomes \(S - 5n = 77\). We now have the system of equations: \[ S + 8n = 207 \quad \text{(1)} \] \[ S - 5n = 77 \quad \text{(2)} \] Subtract equation (2) from equation (1): \[ (S + 8n) - (S - 5n) = 207 - 77 \] Simplifying: \[ 8n + 5n = 130 \quad \Rightarrow \quad 13n = 130 \quad \Rightarrow \quad n = 10 \] Substitute \(n = 10\) into equation (1): \[ S + 8(10) = 207 \quad \Rightarrow \quad S + 80 = 207 \quad \Rightarrow \quad S = 127 \] Now, the mean of the 'n' numbers is: \[ \text{Mean} = \frac{S}{n} = \frac{127}{10} = 12.7 \] Thus, the correct answer is 12.7.