Question : The average of 25 numbers is 64. The averages of the first 13 numbers and that of the last 13 numbers are 62.8 and 72.2, respectively. If the $12^{\text {th }}$ number is 61, and if the $12^{\text {th }}$ and $13^{\text {th }}$ numbers are excluded, then what is the average of the remaining numbers (correct to one decimal place)?
Option 1: 59.2
Option 2: 62.2
Option 3: 60.2
Option 4: 61.5
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Correct Answer: 60.2
Solution : Sum of the 25 numbers = 64 × 25 = 1600 Sum of the first 13 numbers = 13 × 62.8 = 816.4 Sum of the last 13 numbers = 13 × 72.2 = 938.6 Number 13th = (Sum of the first 13 numbers + Sum of the last 13 numbers) – (Sum of the 25 numbers) = (816.4 + 938.6) – (1600) = 1755 – 1600 = 155 The sum of the 23 numbers = (1600 – 155 – 61) = 1384 Average of the 23 numbers = $\frac{1384}{23}$ = 60.17 or 60.2 (approx.) Hence, the correct answer is 60.2.
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