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The average of eight numbers is 14. The average of six of these numbers is 16. The average of the remaining two numbers is:
16
12
8
4
8
Calculate the total sum (8 × 14 = 112) and the partial sum (6 × 16 = 96). Subtract the partial sum from the total sum (112 - 96 = 16) and divide by the remaining 2 numbers (16 / 2 = 8).
Average of 8 numbers = 14. Average of 6 of these numbers = 16.
Sum=Average×Count
Calculate the total sum (8 × 14 = 112) and the partial sum (6 × 16 = 96). Subtract the partial sum from the total sum (112 - 96 = 16) and divide by the remaining 2 numbers (16 / 2 = 8).
Many students multiply the given averages incorrectly or forget to divide the final difference by the count of the remaining numbers (2).
Calculate total sum of 8 numbers
The sum of 8 numbers is given by the product of their count and average.
Sum8=8×14=112
Calculate sum of 6 numbers
Similarly, the sum of 6 of these numbers is calculated.
Sum6=6×16=96
Calculate remaining sum and average
Subtract the sum of 6 numbers from the total sum and divide by the remaining 2.
Averageremaining=2112−96=216=8
C is correct because the average of the remaining two numbers is calculated as (112 - 96) / 2 = 8.
This concept is a precursor to weighted averages often found in mixture and allegation problems in competitive exams.
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