Question
The sum of the digits of a two-digit number is 10. When
the digits are interchanged, the new number is 18 more than the original number. Find the original number.Solution
Let the two-digit number be 10a + b, where a is tens digit and b is units digit. Given: a + b = 10 ...(1) Reversed number = 10b + a New number − original number = 18: (10b + a) − (10a + b) = 18 10b + a − 10a − b = 18 9b − 9a = 18 b − a = 2 ...(2) From (1) and (2): a + b = 10 b − a = 2 Add both: 2b = 12 → b = 6 Then a = 10 − 6 = 4 Original number = 10a + b = 40 + 6 = 46
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