Question

The arithmetic mean of a few numbers is 40. If each number is increased by 7, and then multiplied by 12, then the new mean will be:

• A. 47
• B. 480
• C. 84
• D. 564

Hint:

When numbers are increased by a constant and then multiplied by a constant, the mean is affected by both operations. First add the increase to the sum, then multiply the result.

Answer 1

The Correct Option is D

Let the number of numbers be \( n \), and their sum be \( S \). The arithmetic mean is given by: \[ \frac{S}{n} = 40 \quad \Rightarrow \quad S = 40n. \] When each number is increased by 7, the new sum becomes: \[ S + 7n = 40n + 7n = 47n. \] Then, multiplying the sum by 12: \[ 12 \times (S + 7n) = 12 \times 47n = 564n. \] Thus, the new mean is: \[ \frac{12 \times (S + 7n)}{n} = \frac{564n}{n} = 564. \]