Two-digit number from digit conditions: The number obtained by interchanging the digits of a two-digit number is 18 more than the original number, and the sum of the digits is 8. Find the original number.

Introduction / Context:
Digit puzzles translate directly into small linear equations. Represent the two-digit number as 10a + b with a as the tens digit and b as the units digit. Use the reverse condition and the digit sum to form two equations and solve for a and b.

Given Data / Assumptions:

• Reverse number = original number + 18.
• Sum of digits = 8.
• Digits a, b are integers from 0–9 with a ≥ 1 for a two-digit number.

Concept / Approach:
Let original = 10a + b; reverse = 10b + a. Then 10b + a = 10a + b + 18 and a + b = 8. Solve simultaneously for a and b, ensuring valid digit constraints.

Step-by-Step Solution:

Verification / Alternative check:
Reverse is 53; 53 − 35 = 18 (fits). Digit sum 3 + 5 = 8 (fits).

Why Other Options Are Wrong:
50, 51, 53, 44 do not satisfy both the reverse-difference and digit-sum conditions together.

Common Pitfalls:
Mixing up which number is larger (original vs reverse) and sign errors when rearranging 10b + a = 10a + b + 18 are common mistakes.

Final Answer:
35