Final answer:
The four numbers in the ratio 9:11 are 27, 33, 33, and 33. None of the given ratios match these numbers.
Step-by-step explanation:
The ratio between the four numbers is given as 9:11 and their difference is 6. To find the four numbers, we need to determine a common factor between 9 and 11. The only common factor is 1, so we can multiply both parts of the ratio by 1 to get 9:11. This means that the two numbers in the ratio are 9x and 11x, where x is a common factor. We also know that the difference between these two numbers is 6, so we can set up the equation 11x - 9x = 6 and solve for x. In this case, x = 3. Therefore, the four numbers are 9(3) = 27, 11(3) = 33, 11(3) = 33, and 11(3) = 33. This corresponds to the ratio 27:33:33:33. None of the given ratios a) 33:44, b) 45:55, c) 21:27, or d) 15:19 match the ratio of the four numbers derived from the given information. Therefore, the correct answer is none of the above.