To solve this problem, we need to understand the concept of averages. The average of a set of numbers is the sum of all the numbers divided by the total number of numbers.

In this question, we are given that the average of x, y, and z is 30. Let`s assume that there are a total of n numbers in the set. So, the sum of x, y, and z would be 30n.

We are also given that the average of x and y is 20. This means that the sum of x and y would be 20 multiplied by 2, which equals 40.

To find the value of z, we can subtract the sum of x and y from the sum of x, y, and z. So, it would be 30n - 40.

Since we do not have the exact values of x, y, or z, we cannot determine the exact value of z. Therefore, none of the options provided, (option 1: 10, option 2: 20, option 3: 40, option 4: 50), can be confidently considered the correct answer.

Alert - correct answer should be "Cannot be determined"