Question

When 3 is subtracted from each of the given 'n' numbers, then the sum of the numbers so obtained is 84. When 8 is added to each of the given 'n' numbers, then the sum of the resulting numbers is 216. The mean of the given 'n' numbers is:

• A. 9.5
• B. 12
• C. 12.5
• D. 10

Hint:

When comparing changes to a total due to constant addition or subtraction, use system of equations to find original values.

Answer 1

The Correct Option is D

Let the sum of the original 'n' numbers be \( S \). Then, \[ S - 3n = 84 \quad \text{(i)}
S + 8n = 216 \quad \text{(ii)} \] Subtracting (i) from (ii): \[ (S + 8n) - (S - 3n) = 216 - 84
11n = 132 \Rightarrow n = 12 \] Substitute back into (i): \[ S - 36 = 84 \Rightarrow S = 120 \] Mean \( = \frac{S}{n} = \frac{120}{12} = 10 \) Correct value: 10