Question
The average of 22 numbers is 90. The average of the
first 14 numbers is 95, while the average of the last 10 numbers is 85. If the 14th number is removed, what will be the average of the remaining 21 numbers, rounded to one decimal place?Solution
ATQ, Sum of 22 numbers = 90 × 22 ⇒ 1980 Sum of first 14 numbers = 95 × 14 ⇒ 1330 Sum of last 10 numbers = 10 × 85 ⇒ 850 Let the 14th number be x Sum of 22 numbers = Sum of first 14 numbers + Sum of last 10 numbers - 14th number ⇒ 1980 = 1330 + 850 - x ⇒ 1980 = 2180 - x ⇒ x = 2180 - 1980 ⇒ x = 200 Sum of remaining numbers = 1980 - 200 ⇒ 1780 Remaining numbers = 21 Average of remaining numbers = 1780 / 21 ⇒ 84.8 ∴ The average of the remaining numbers (correct to one decimal place) is 84.8
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