Explanation:

To solve this, let's start logically breaking down the problem:

- The numbers are in the ratio 1:2:3:5. Let's denote the numbers as \(x, 2x, 3x, 5x\).

- The sum of these numbers is \(x + 2x + 3x + 5x = 11x\).

- Two times their sum is 44, so \(2 \times 11x = 44\).

- Solving \(22x = 44\), we get \(x = 2\).

Now, calculate each number:

- The numbers are \(2, 4, 6, 10\).

Subtract 3 from the cube of each number:

- \(2^3 - 3 = 8 - 3 = 5\)

- \(4^3 - 3 = 64 - 3 = 61\)

- \(6^3 - 3 = 216 - 3 = 213\)

- \(10^3 - 3 = 1000 - 3 = 997\)

The ratio of these results is 5:61:213:997.

Now, let's check the options:

- Option 1: 2 : 31 : 204 : 999

- Option 2: 3 : 13 : 208 : 992

- Option 3: 11 : 67 : 219 : 1003

- Option 4: 5 : 61 : 213 : 997

- ? Option 4: 5 : 61 : 213 : 997 is the correct ratio.