Explanation:

- We know the product of the two positive numbers is 240.

- We also know that the ratio of the two numbers is 3:5.

- Let's denote the numbers as \(3x\) and \(5x\).

- Their product is \(3x \times 5x = 240\).

- Solving \(15x^2 = 240\) gives \(x^2 = 16\).

- So, \(x = 4\).

- Therefore, the numbers are \(3x = 12\) and \(5x = 20\).

- The sum of the two numbers is \(12 + 20 = 32\).

Now let's consider the options:

- Option 1: 46

- Option 2: 45

- Option 3: 32

- Option 4: 42

The correct option is 3, and the sum is indeed 32.