The average of the eight numbers is 32. The first two numbers average 28.5 and the next three numbers average 30. The 6th number is 50% more than the 8th number but 5 less than the 7th number. What is the average of the 6th and 8th numbers?

The average of the eight numbers is 32. The first two numbers average 28.5 and the next three numbers average 30. The 6th number is 50% more than the 8th number but 5 less than the 7th number. What is the average of the 6th and 8th numbers? Correct Answer 32.5

Given:

The average of 8 number is 32

Concept:

The average = (The sum of all items)/(Total number of items)

Calculation:

⇒ Total sum of 8 number = 32 × 8 = 256

⇒ The sum of the first two number = 28.5 × 2 = 57

⇒ The sum of the next three number = 30 × 3 = 90

⇒ Let be assume 6^th, 7^th, and 8^th number is p, q, and r respectively.

⇒ p = (3/2) × r

⇒ p = q - 5

⇒ (3/2) × r + 5 = q

⇒ p + q + r = 256 - 57 - 90 = 109

⇒ p + 1.5 × r + 5 + r = 109

⇒ p + 2.5 × (2/3) × p = 109 - 5

⇒ 3p + 5p = 3 × 104

⇒ p = 39, r = 26

⇒ The average of p and r = (39 + 26)/2 = 32.5

∴ The required result will be 32.5.