Correct Answer - Option 2 : 76

**Formula:**

Average = (Sum of elements)/(Number of elements)

**Calculation:**

Let four consecutive even natural numbers be a, a + 2, a + 4 and a + 6 respectively.

Total sum of squares of four consecutive even natural numbers = 126 × 4 = 504

⇒ a^{2} + (a + 2)^{2} + (a + 4)^{2} + (a + 6)^{2} = 504

⇒ 4a^{2} + 24a - 448 = 0

⇒ a^{2} + 6a - 112 = 0

⇒ a^{2} + 14a - 8a - 112 = 0

⇒ a(a + 14) - 8(a + 14) = 0

⇒ (a + 14)(a - 8) = 0

a = -14 or a = 8

a is a even natural number so a = 8

Greatest number = 8 + 6 = 14

Smallest number = 8

Then,

8 times of greatest number = 14 × 8 = 112

5 times of smallest number = 8 × 5 = 40

**∴ average of 8 times of the greatest number and 5 times of the smallest number = (112 + 40)/2 = 76**