Question

The average of four consecutive odd natural numbers is eight less than the average of three consecutive even natural numbers. If the sum of these three even numbers is equal to the sum of above four odd numbers, then the average of four original odd numbers is:
1. 24
2. 18
3. 32
4. 36

Answer 1

Correct Answer - Option 1 : 24

Given:

Average of four consecutive odd natural numbers is eight less than the average of three consecutive even natural numbers,

The sum of these three even numbers is equal to the sum of above four odd numbers

Formula used:

\(Average=(Sum of all numbers)/(total numbers)\)

Calculation:

Four consecutive odd natural number is

⇒ X₁ – 2, X₁, X₁ + 2 and X₁ + 4

Average = (X₁ – 2 + X₁ + X₁ + 2 + X₁ + 4)/4

⇒ (4X₁ + 4)/4

⇒ X₁ + 1

Three consecutive even natural numbers is

⇒ X₂ – 2, X₂, X₂ + 2

Average = (X₂ – 2 + X₂ + X₂ + 2)/3

⇒ 3X₂/3

⇒ X₂

According to question

⇒ X₁ + 1 = X₂ – 8

⇒ X₁ – X₂ = -9      ….(i)

And the sum of these three even numbers is equal to the sum of above four odd numbers

⇒ X₂ – 2 + X₂ + X₂ + 2 = X₁ – 2 + X₁ + X₁ + 2 + X₁ + 4

⇒ 3X₂ = 4X₁ + 4

⇒ 3X₂ - 4X₁ = 4      ….(ii)

Solve the equation (i) and (ii),

  ⇒ X₁ = 23 and X₂ = 32

Average of odd number = X₁ + 1

⇒ 23 + 1

⇒ 24

∴ Average of odd number is 24