Explanation:

Alright, let’s break this down step by step:

- The average of 11 numbers is 68. Total: 11 × 68 = 748.

- The average of the first four is 78. Total for them: 4 × 78 = 312.

- The average of the next four is 63. Total for them: 4 × 63 = 252.

- So, the sum of the first 8 is 312 + 252 = 564.

- That leaves: 748 - 564 = 184 for numbers 9, 10, and 11.

Now, let's go further:

- 9th = 2 × 11th (let’s say 9th = 2x, 11th = x, 10th = y < x)

- So, 2x + y + x = 184 ? 3x + y = 184.

They want the average of 9th and 11th:

- (2x + x)/2 = (3x)/2.

Let’s check the options for x:

- Since y < x, and 3x + y = 184, pick x so that y < x.

Try x = 46 (so 2x = 92, x = 46, total 2x + x = 138, subtract from 184: 184 - 138 = 46; y = 46, but y can’t be equal to x, it must be less).

- Try x = 47.

- 9th: 94, 11th: 47, 10th: 184 - 94 - 47 = 43, which is less than 47.

- Good! Let's find the average of 9th and 11th: (94 + 47)/2 = 141/2 = 70.5.

Let’s check which option matches:

- Option 4, 70.5 is correct.

What this really means is, the 9th is 94, 11th is 47, their average is 70.5.

So, your logic checks out. If you ever want to see the math worked out another way, feel free to ask!