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    Question

    The sum of the digits of a two-digit number is 9. If 27

    is subtracted from the number, its digits switch their places. What is the number?
    A 63 Correct Answer Incorrect Answer
    B 56 Correct Answer Incorrect Answer
    C 70 Correct Answer Incorrect Answer
    D 65 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the unit digit be 'a' and tens digit be 'b'.

    Original number = 10b + a

    Reversed number = 10a + b

    Given:

    a + b = 9 --------- (I)

    10b + a - 27 = 10a + b

    ⇒ 9b - 9a = 27

    ⇒ b - a = 3 --------- (II)

    Add equations (I) and (II):

    a + b + b - a = 9 + 3

    ⇒ 2b = 12 ⇒ b = 6

    Then a = 9 - 6 = 3

    Required number = 10 × 6 + 3 = 63

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