The average of 16 numbers is 82. The average of the first 8 numbers is 90, while the average of the last 9 numbers is 75. If the 8th number is removed, what will be the average of the remaining 15 numbers, rounded to one decimal place?

ATQ, Sum of 16 numbers = 82 × 16 ⇒ 1312 Sum of first 8 numbers = 90 × 8 ⇒ 720 Sum of last 9 numbers = 9 × 75 ⇒ 675 Let the 8th number be x Sum of 16 numbers = Sum of first 8 numbers + Sum of last 9 numbers - 8th number ⇒ 1312 = 720 + 675 - x ⇒ 1312 = 1395 - x ⇒ x = 1395 - 1312 ⇒ x = 83 Sum of remaining numbers = 1312 - 83 ⇒ 1229 Remaining numbers = 15 Average of remaining numbers = 1229 / 15 ⇒ 81.9 ∴ The average of the remaining numbers (correct to one decimal place) is 81.9