Introduction:
In this problem, we are given the task to find the number of three-digit numbers that are divisible by 5 or 9. We need to choose the correct option from the given choices.

Solution:
To solve this problem, we need to find the count of three-digit numbers that are divisible by 5 and the count of three-digit numbers that are divisible by 9. Then, we can add these two counts to get the final answer.

Count of three-digit numbers divisible by 5:
To find the count of three-digit numbers divisible by 5, we need to determine the range of three-digit numbers divisible by 5 and then divide this range by 5.

The smallest three-digit number divisible by 5 is 100, and the largest three-digit number divisible by 5 is 999. To find the count of numbers divisible by 5 in this range, we can subtract the smallest number from the largest number and add 1, and then divide the result by 5.

Count of three-digit numbers divisible by 5 = (999 - 100 + 1) / 5 = 900 / 5 = 180

Count of three-digit numbers divisible by 9:
To find the count of three-digit numbers divisible by 9, we need to determine the range of three-digit numbers divisible by 9 and then divide this range by 9.

The smallest three-digit number divisible by 9 is 108, and the largest three-digit number divisible by 9 is 999. To find the count of numbers divisible by 9 in this range, we can subtract the smallest number from the largest number and add 1, and then divide the result by 9.

Count of three-digit numbers divisible by 9 = (999 - 108 + 1) / 9 = 891 / 9 = 99

Total count:
To get the total count of three-digit numbers divisible by 5 or 9, we add the count of three-digit numbers divisible by 5 and the count of three-digit numbers divisible by 9.

Total count = Count of three-digit numbers divisible by 5 + Count of three-digit numbers divisible by 9
= 180 + 99
= 279

Therefore, the correct option is 'A' (260).