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    Question

    The sum of the digits of a two-digit number is 7. If 45

    is subtracted from this number, the resulting number has its digits reversed. Determine the original number.
    A 61 Correct Answer Incorrect Answer
    B 52 Correct Answer Incorrect Answer
    C 16 Correct Answer Incorrect Answer
    D 25 Correct Answer Incorrect Answer

    Solution

    Let ones and tens digit of the number be 'a' and 'b' respectively.

    So, original number = 10b + a

    Reverse number = 10a + b

    So, a + b = 7 --------- (I)

    And, 10b + a - 45 = 10a + b

    Or, 9b - 9a = 45

    Or, b - a = 5 ---------- (II)

    On adding equation I and II,

    We get, a + b + b - a = 7 + 5

    Or, 2b = 12

    Or, 'b' = 6

    On putting value of 'b' in equation I,

    We get, 6 + a = 7

    Or, 'a' = 1

    Required number = 10 x 6 + 1 = 61

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