The sum of the digits of a certain two-digit number is 9. Reversing its digits decreases the number by 81. What is the number?

Question

It is a confusing question.

Answer 1

Every two-digit number x can be written as x = 10*a + b. In that case we have:

a + b =9 and

10*b + a = x - 81 or 10*b + a = 10*a + b - 81.

If we rearranged the second part we obtain 9*b - 9*a = -81 or equivalently: a - b =9. So all we need is to solve for the system:

a + b = 9

a - b = 9

which means a=9 and b=0 or x=90.