The difference between a two-digit number and the number obtained by interchanging its digits is 36. What is the difference between its two digits?

Problem restatementA two-digit number (tens digit a, units digit b) exceeds its reverse by 36. Find |a − b|.

Given data

• Original number = 10a + b
• Reversed number = 10b + a
• Difference = (10a + b) − (10b + a) = 36

Concept/ApproachSimplify the difference to get a linear equation in (a − b).

Step-by-step calculation (10a + b) − (10b + a) = 9(a − b) = 36 a − b = 36 ÷ 9 = 4

Verification/AlternativeIf a − b = 4, then 9(a − b) = 36 exactly as given.

Common pitfalls

• Using b − a instead of a − b; the absolute difference is 4 in any case.

Final Answer4