The average of 11 numbers is 68. The average of the first four numbers is 78 and that of the next four numbers is 63. The 9th is two times the 11th number and the 10th number is 4 less than the 11th number. what is the average of 9th and 11th numbers?

Let the 11th number be x. Then 9th number = 2x and 10th number = x - 4. Sum of first 8 numbers = 4×78 + 4×63 = 312 + 252 = 564. Sum of all 11 numbers = 11×68 = 748. Sum of 9th, 10th, 11th = 748 - 564 = 184. So: 2x + (x - 4) + x = 184 → 4x - 4 = 184 → 4x = 188 → x = 47. 9th = 2×47 = 94, 11th = 47. Average of 9th and 11th = (94 + 47)/2 = 141/2 = 70.5.