Explanation:

- The average of five numbers (20, 40, 50, Y, and Z) is 45.

- To find the total sum of these numbers, multiply their average by the count:

$$\text{Total Sum}=45\times 5=225$$

- The sum of known numbers is:

$$20+40+50=110$$

- Therefore, the sum of Y and Z is:

$$225-110=115$$

- To find the average of Y and Z:

$$\text{Average of Y and Z}=\frac{115}{2}=57.5$$

- Option 1: 58.5 (Incorrect)

- Option 2: 57.5 (Correct)

- Option 3: 56.5 (Incorrect)

- Option 4: 55 (Incorrect)