The question goes as follows:
Let $K$ be a three digit number such that the ratio of the number to the sum of its digit is least. What is the difference between the hundreds and the tens digits of $K$?
Now I was able to do this question by trial and error, assuming hundredth digit place to be 1 and unit as well as tens digit to be 9
So the number is 199, but I am not able to do it logically, any way to do it?