When 18 is included in a list of natural numbers, the average of these numbers is increased by 2. When 8 is included in this new list of natural numbers, the average of these numbers in the new list remains the same. If there are N natural numbers in the original list of numbers and their average is X, find the value of N and X, respectively.

Question

Question

This question was previously asked in

UGC NET Official Paper 1: Held On 15 June 2023 Shift 1

Answer 1

Calculation:

According to the question,

(Nx + 18) = (N + 1) × (x + 2)

⇒ Nx + 18 = Nx + 2N + x + 2

⇒ 2N + x = 16

⇒ (N + x)+ N = 16 … (i)

Again, (Nx + 18 + 8) = (N + 2) × (x + 2)

⇒ Nx + 26 = Nx + 2N + 2x + 4

⇒ 2N + 2x = 22

⇒ N + x = 11, put the value in equation (i) we get,

11 + N = 16

⇒ N = 5 now put the value in equation (i), we get x = 6

∴ The correct answer is 5, 6