The average of thirteen numbers is 57. The average of first three numbers is 48, and that of the next seven numbers is 58. The 11th number is two times the 12th number and 12th number is 3 less than the 13th number. What is the average of the 11th and 13th numbers?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 72.
Total sum = 13 × 57 = 741
Sum of first 3 = 3 × 48 = 144
Sum of next 7 = 7 × 58 = 406
Sum of last 3 = 741 - 144 - 406 = 191
Let 13th = x
12th = x - 3
11th = 2(x - 3) = 2x - 6
Sum = 2x - 6 + x - 3 + x = 4x - 9 = 191
4x = 200 → x = 50
11th = 94, 13th = 50
Average = (94 + 50) / 2 = 72