The average of 21 numbers is 74. The average of the first 11 numbers is 72.8 and that of the last 11 numbers is 77.2. If the 10th number is five less than the 11th number and if 10th and 11th numbers are excluded, then what is the average of the remaining numbers? (correct to nearest integer)
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 72.
Total sum = 21 × 74 = 1554
Sum of first 11 = 11 × 72.8 = 800.8
Sum of last 11 = 11 × 77.2 = 849.2
Sum of first 11 + last 11 = 800.8 + 849.2 = 1650
But this counts the 11th number twice, so:
11th number = 1650 − 1554 = 96
10th number = 96 − 5 = 91
Sum excluding 10th and 11th = 1554 − (91 + 96) = 1367
Average of remaining 19 numbers = 1367 ÷ 19 = 72