If the average of 5 consecutive even numbers is 10 , then find the number at the centre when these five numbers are arranged in ascending order.

Correct option is D

Given:
The average of 5 consecutive even numbers is 10.

Formula Used:

​$$\text{Average} = \frac{\text{Sum of numbers}}{\text{Count of numbers}}$$

Solution:

Let the 5 consecutive even numbers be (x-4), (x-2), x, (x+2), (x+4).

Sum of numbers = (x-4) + (x-2) + x + (x+2) + (x+4) = 5x

​$$\text{Average} = \frac{\text{Sum of numbers}}{\text{Count of numbers}} \implies \frac{5x}{5} = x$$

Average of 5 consecutive even numbers is 10.

x = 10.

5 consecutive even numbers are 6, 8, 10, 12, 14

The number at the center is 10.