Two-digit number puzzle — the digits sum to 11. Adding 27 reverses the digits. What is the original number?

Introduction / Context:
This number puzzle involves digit algebra for a two-digit number. The sum of the digits is fixed, and adding a constant reverses the digit order. Translate into equations using tens and units digits, then solve systematically.

Given Data / Assumptions:

• Let tens digit = a; units digit = b.
• Original number = 10a + b.
• a + b = 11.
• 10a + b + 27 = 10b + a (reversed digits after adding 27).

Concept / Approach:
Use the reversal condition to form a linear equation in a and b. Combine it with the digit-sum equation to find unique integer digits 0–9 that satisfy both constraints.

Step-by-Step Solution:

Verification / Alternative check:
47 + 27 = 74, which is indeed the reversal of 47. Digit sum 4 + 7 = 11 holds. All conditions satisfied.

Why Other Options Are Wrong:

• 65, 83, 92 — do not meet both the digit-sum and “+27 reverses digits” conditions.

Common Pitfalls:
Mixing tens and units roles or misreading “reversal.” Always write the two equations explicitly to avoid mistakes.

Final Answer:
47