Question
The sum of the digits of a two-digit number is 11. When
the digits are reversed, the new number is 27 more than the original number. Find the original number.Solution
Let the original number be 10a + b, where a is tens digit and b is units digit. Given: a + b = 11 ...(1) Reversed number = 10b + a, and 10b + a = (10a + b) + 27 10b + a = 10a + b + 27 9b − 9a = 27 b − a = 3 ...(2) From (1) and (2): a + b = 11 b − a = 3 Add: 2b = 14 ⇒ b = 7 Then a = 11 − 7 = 4 Original number = 10a + b = 40 + 7 = 47
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