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 β¦(1) Interchanging digits β new number = 10y + x Given: 10y + x = 10x + y + 27 β 9y β 9x = 27 β y β x = 3 β¦(2) From (1) and (2): x + y = 11 y β x = 3 Adding: 2y = 14 β y = 7 Then x = 11 β 7 = 4 Number = 47.
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