Question
The sum of the digits of a two-digit number is 11. When
the digits are interchanged, the new number is 27 more than the original number. What is the original number?Solution
ATQ, Let the number be 10x + y, where x is tens digit and y is units digit. x + y = 11 …(1) Interchanging digits → new number = 10y + x Given: 10y + x = 10x + y + 27 ⇒ 9y – 9x = 27 → y – x = 3 …(2) From (1) and (2): x + y = 11 y – x = 3 Adding: 2y = 14 → y = 7 Then x = 11 – 7 = 4 Number = 47.
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