Question

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the largest and the smallest of these two digits?

Answer 1

let original number be 10x + y
then the number reversed is 10y + x

difference= 10x+y - (10y+x)
= 9x - 9y
but
9x - 9y= 36
x - y = 4
since x and y must both be integers between 1 and 9
that little equation tells me that the difference between the digits is 4


possible (x,y) are
(9,5), (8,4), (7,3), (6,2) and (5,1)
the difference between the digits for all of them is 4
e.g.
suppose x = 7, y = 3
the first number is 73, and the number reversed is 37
notice 73 - 37 = 36