Question
The average of 28 numbers is 50. The average of the
first 16 numbers is 55, while the average of the last 13 numbers is 45. If the 16th number is removed, what will be the average of the remaining 27 numbers, rounded to one decimal place?Solution
ATQ, Sum of 28 numbers = 50 × 28 ⇒ 1400 Sum of first 16 numbers = 55 × 16 ⇒ 880 Sum of last 13 numbers = 13 × 45 ⇒ 585 Let the 16th number be x Sum of 28 numbers = Sum of first 16 numbers + Sum of last 13 numbers - 16th number ⇒ 1400 = 880 + 585 - x ⇒ 1400 = 1465 - x ⇒ x = 1465 - 1400 ⇒ x = 65 Sum of remaining numbers = 1400 - 65 ⇒ 1335 Remaining numbers = 27 Average of remaining numbers = 1335 / 27 ⇒ 49.4 ∴ The average of the remaining numbers (correct to one decimal place) is 49.4
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