Question

When 5 is subtracted from each of given \( n \) numbers, the sum of numbers so obtained is 210. When 8 is subtracted from each of the given \( n \) numbers, then the sum of numbers so obtained is 156. What is the mean of the given \( n \) numbers?

• A. \( \frac{15}{3} \)
• B. \( \frac{16}{3} \)
• C. 15
• D. 17

Hint:

When dealing with sums and means, set up equations based on the sum of numbers and solve for the unknown.

Answer 1

The Correct Option is C

Let the mean of the \( n \) numbers be \( x \). The sum of all the numbers is \( n \times x \). When 5 is subtracted from each number, the sum becomes \( n \times (x - 5) = 210 \). When 8 is subtracted from each number, the sum becomes \( n \times (x - 8) = 156 \). Solving these two equations, we find \( x = 15 \).