Explanation:

Let's solve step by step:

- Let x and y be positive numbers.

- When x is reduced by 2, and y is increased by 2, the ratio is 2:1:

$$(x - 2) / (y + 2) = 2/1$$

\(\rightarrow x - 2 = 2(y + 2)\)

\(\rightarrow x - 2 = 2y + 4\)

\(\rightarrow x - 2y = 6\)

- When x is increased by 2, and y is reduced by 2, the ratio is 3:1:

$$(x + 2) / (y - 2) = 3/1$$

\(\rightarrow x + 2 = 3(y - 2)\)

\(\rightarrow x + 2 = 3y - 6\)

\(\rightarrow x - 3y = -8\)

- Solving the two equations:

1. \(x - 2y = 6\)

2. \(x - 3y = -8\)

- Subtract the second from the first:

$$(x - 2y) - (x - 3y) = 6 - (-8)$$

$$x - 2y - x + 3y = 14$$

$$y = 14$$

- Plug back into the first equation:

\(x - 2(14) = 6 \Rightarrow x - 28 = 6 \Rightarrow x = 34\)

- So, \(x - y = 34 - 14 = 20\)

- Checking the options:

- 1. 20

- 2. 24

- 3. 18

- 4. 22

Correct Answer is: Option 1 — 20

- Both statements are satisfied with these values for x and y.

- Other options do not fit the calculated difference.