Question

The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original number. What is the original number?
26
35
53
62

Answer 1

Let the tens digit be t and the units digit be u. Then
t + u = 8
and reversing gives 10u + t = 10t + u − 18.
Simplify the second: 9u − 9t = −18 → u − t = −2 → u = t − 2.
Substitute into the sum: t + (t − 2) = 8 → 2t = 10 → t = 5, u = 3.
The original number is 53.