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    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.
    A 32 Correct Answer Incorrect Answer
    B 47 Correct Answer Incorrect Answer
    C 27 Correct Answer Incorrect Answer
    D 65 Correct Answer Incorrect Answer

    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 тИТ 9a = 27 b тИТ a = 3 ...(2) From (1) and (2): a + b = 11 b тИТ a = 3 Add: 2b = 14 тЗТ b = 7 Then a = 11 тИТ 7 = 4 Original number = 10a + b = 40 + 7 = 47

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