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    Question

    A two-digit number has a sum of its digits equal to 9.

    Additionally, if 27 is subtracted from this number, the resulting number has its digits reversed. What is the original number?
    A 48 Correct Answer Incorrect Answer
    B 58 Correct Answer Incorrect Answer
    C 63 Correct Answer Incorrect Answer
    D 73 Correct Answer Incorrect Answer

    Solution

    ATQ,

    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 = 9 --------- (I)

    And, 10b + a - 27 = 10a + b

    Or, 9b - 9a = 27

    Or, b - a = 3 ---------- (II)

    On adding equation I and II,

    We get, a + b + b - a = 9 + 3

    Or, 2b = 12

    Or, 'b' = 6

    On putting value of 'b' in equation I,

    We get, 6 + a = 9

    Or, 'a' = 3

    Required number = 10 × 6 + 3 = 63

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