Two-digit number with digit relation and reversal effect: The units digit is 1 less than twice the tens digit. After interchanging the digits, the difference (new − original) is 20 less than the original number. Find the original number.

Introduction / Context:This problem combines a digit relationship with a condition on the difference between the reversed number and the original. Setting up algebra for digits and using the reversal difference formula make it tractable.

Given Data / Assumptions:

• Tens digit = t; Units digit = u.
• u = 2t − 1.
• After swapping digits, difference (new − original) is less than the original by 20 ⇒ (new − original) = original − 20.

Concept / Approach:Original = 10t + u; New = 10u + t. Then (new − original) = 9(u − t). Combine this with the linear relation u = 2t − 1 and the “less by 20” equation to solve for t.

Step-by-Step Solution:

Verification / Alternative check:Reversed is 74. new − original = 74 − 47 = 27; original − 20 = 47 − 20 = 27. Condition holds exactly.

Why Other Options Are Wrong:

• 59, 23, 35, 41: They fail either the digit relation u = 2t − 1 or the “difference” condition.

Common Pitfalls:Misinterpreting “less than the original by 20” as subtracting 20 from the new number. Carefully equate (new − original) to (original − 20).

Final Answer:47