Two-Digit Number with Units Digit Tied to Tens Digit A two-digit number has its units digit equal to (2 × tens digit) + 1. After interchanging the digits, the difference between the new number and the original equals the original number minus 1. What is the original number?

Introduction / Context:
This digit puzzle encodes the number's structure into algebra. Recognizing the standard difference formula for reversed two-digit numbers accelerates the solution: (10b + a) − (10a + b) = 9(b − a).

Given Data / Assumptions:

• Let number be 10a + b with digits a (tens) and b (units).
• Digit rule: b = 2a + 1.
• After reversing digits, difference (new − original) equals (original − 1).

Concept / Approach:
Use the reversal difference identity and substitute the linear relation between b and a. Solve for a and b in digit range constraints (a from 1 to 9, b from 0 to 9).

Step-by-Step Solution:
Difference after reversal: 9(b − a).Given: 9(b − a) = (10a + b) − 1.Substitute b = 2a + 1: LHS = 9((2a + 1) − a) = 9a + 9; RHS = 10a + (2a + 1) − 1 = 12a.Equation: 9a + 9 = 12a → 3a = 9 → a = 3.Then b = 2*3 + 1 = 7 → number = 37.

Verification / Alternative check:
Reverse 37 → 73; difference 73 − 37 = 36; original − 1 = 37 − 1 = 36. Both conditions hold.

Why Other Options Are Wrong:
52, 25, and 39 do not satisfy b = 2a + 1; 73 is the reversed number, not the original.

Common Pitfalls:
Misinterpreting the difference statement, or using b = 2a − 1 instead of b = 2a + 1.

Final Answer:
37