The average of 25 numbers is 64. The average of the first 13 numbers and that of the last 13 numbers are 62.8 and 72.2, respectively. If the 12th number is 61, and if the 12th and 13th numbers are excluded, then what is the average of the remaining number (correct to one decimal place)?

Answer: Option C

Average of 25 numbers = 64
Sum of 25 numbers = 64 × 25 = 1600
Average of first 13 numbers = 62.8
Sum of first 13 numbers = 62.8 × 13 = 816.4
Average of last 13 numbers = 72.2
Sum of last 13 numbers = 72.2 × 13 = 938.6
13^th number = 816.4 + 938.4 - 1600
= 1754.8 - 1600
= 154.8
12^th number = 61
If we remove 12^th and 13^th number then, sum of remaining numbers = 1600 - 61 - 154.8 = 1384.2
Average $$=\frac{1384.2}{23}=60.18\sim 60.2$$