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    Question

    A two-digit number has a sum of its digits equal to 12.

    Additionally, if 45 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 75 Correct Answer Incorrect Answer
    E None of these 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 = 12 --------- (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 = 12 + 5

    Or, 2b = 17

    Or, 'b' = 7

    On putting value of 'b' in equation I,

    We get, 7 + a = 12

    Or, 'a' = 5

    Required number = 10 × 7 + 5 = 75

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