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    Question

    A two-digit number has a sum of its digits equal to 11.

    Additionally, if 54 is subtracted from this number, the resulting number has its digits reversed. What is the original number?
    A 53 Correct Answer Incorrect Answer
    B 93 Correct Answer Incorrect Answer
    C 83 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 = 11 --------- (I)

    And, 10b + a - 54 = 10a + b

    Or, 9b - 9a = 54

    Or, b - a = 6 ---------- (II)

    On adding equation I and II,

    We get, a + b + b - a = 11 + 6

    Or, 2b = 17

    Or, 'b' = 8

    On putting value of 'b' in equation I,

    We get, 8 + a = 11

    Or, 'a' = 3

    Required number = 10 × 8 + 3 = 83

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