How many three digit numbers are divisible by 5 or 9 ?

Correct option is B

1. Numbers divisible by 5:

- Smallest number: 100 .
- Largest number: 995 .
- Common difference: 5 .
Using the formula:
​$$n = \frac{l - a}{d} + 1 = \frac{995 - 100}{5} + 1 = 180$$​
So, there are 180 numbers divisible by 5.

2. Numbers divisible by 9:
- Smallest number: 108 .
- Largest number: 999 .
- Common difference: 9 .
Using the formula:
​$$n = \frac{l - a}{d} + 1 = \frac{999 - 108}{9} + 1 = 100$$​
So, there are 100 numbers divisible by 9.

3. Numbers divisible by both 5 and 9:
- These numbers are divisible by the LCM of 5 and 9, which is 45 .
- Smallest number: 108 .
- Largest number: 990 .
- Common difference: 45 
Using the formula:
​$$n = \frac{l - a}{d} + 1 = \frac{990 - 108}{45} + 1 = 20$$​
So, there are 20 numbers divisible by both 5 and 9.

4. Apply the principle of inclusion and exclusion:
Using the formula:
Count = Numbers divisible by 5 + Numbers divisible by 9 - Numbers divisible by both 5 and 9
Count = 180 + 100 - 20 = 260

Final Answer:

The total number of three-digit numbers divisible by 5 or 9 is 260 .