That means we have,

N=100q+r

Substract 99q from both sides to obtain,

(N-99 q) = q+r

Now, we need that q+r to be divisble by 11.

Because of equality it is equivalent to saying,

That we need (N- 99q) to be divisible by 11.

But 99q is already divisible by 11.

Thus, we require that N be divisible by 11.

Thus, what the question isreallyasking is how many 5 digits numbers are divisible by 11.

Let us list all 5 digit numbers in increasing order.

10000

10001

10002

10003

.....

99999

The fist number on this list divisible by 11 is:

10010

And after that each 11-th number is divisble of 11.

Thus,

10010

10021

10032

....

Up to 99999

Now, I leave if to you to figure out how many numbers are in that list.