Explanation:

- The problem starts with a ratio of two numbers, 4:5. Let's call these numbers 4x and 5x.

- When both numbers are increased by 4, the new ratio is 5:6.

- So, (4x + 4) / (5x + 4) = 5/6. Cross-multiplying gives us 6(4x + 4) = 5(5x + 4).

- This expands to 24x + 24 = 25x + 20. Simplifying gives x = 4.

- If x = 4, the original numbers are 16 and 20. Their sum is 36.

- Checking the options:

- Option 1: 9

- Option 2: 18

- Option 3: 27

- Option 4: 36

Your sum of the two numbers is 36.