The two-digit number obtained by interchanging the digits is 54 less than the original number. If the sum of the digits of the original number is 10, what is the original number?

Introduction:
Represent a two-digit number in terms of its tens and units digits. Swapping the digits changes the value predictably. Combine the swap difference with the sum constraint to solve for both digits.

Given Data / Assumptions:

• Let tens digit be t and units digit be u.
• Original number = 10t + u; swapped = 10u + t.
• 10t + u − (10u + t) = 54; t + u = 10.

Concept / Approach:
From the difference equation, derive t − u, then combine with t + u to solve uniquely for digits. Ensure each digit is 0–9 and t ≠ 0 (since it’s a two-digit number).

Step-by-Step Solution:

Verification / Alternative check:
Swapped number 28 is indeed 54 less than 82, and digit sum 8 + 2 = 10.

Why Other Options Are Wrong:
28 and 39 do not satisfy both constraints as the original number; “Cannot be determined” is incorrect because the solution is unique.

Common Pitfalls:
Reversing the difference sign or assuming the smaller number is original.

Final Answer:
82