Question

how many numbers between 5501 and 5600 have the digit 9?

Answer 1

its obvious that there'll be nine in each set of ten numbers(1,2,3,4,5,6,7,8,9,10 ending nos. )
 there are about 10 sets of 10's between 5501 and 5600 i.e 
5501-5510
5511-5520
5521-5530
5531-5540
5541-5550
5551-5560
5561-5570
5571-5580
5581-5590
5591-5600

in each of these sets there is a number that ends with 9
5509,5519,5529,5539,5549,5559,5569,5579,5589,5599

but the tenth set has 9 more 9s as the second digit from right has also 9
5591,5592,5593,5594,5595,5596,5597,5598,5599

so last digit ten 9s and second digit eight 9s has to be summed up.
10+9 = 19

Answer 2

the number between 5501 to 5600 is 159