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 12^th number is 61, and if the 12^th and 13^th numbers are excluded, then what is the average of the remaining number (correct to one decimal place)?

A. 59.2

B. 61.5

C. 60.2

D. 62.2

Answer: Option C

Solution(By Examveda Team)

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 $$ = \frac{{1384.2}}{{23}} = 60.18 \sim 60.2$$