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    Question

    The digits of a two-digit number add up to 9. If 27 is

    subtracted from the number, the digits switch places. What is the number?
    A 63 Correct Answer Incorrect Answer
    B 56 Correct Answer Incorrect Answer
    C 73 Correct Answer Incorrect Answer
    D 65 Correct Answer Incorrect Answer

    Solution

    ATQ,
    Let the digits be 'a' (ones) and 'b' (tens).

    Original number = 10b + a

    Reversed = 10a + b
    Given:

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

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

    ⇒ 9b - 9a = 27

    ⇒ b - a = 3 --------- (II)

    Add (I) and (II):

    a + b + b - a = 9 + 3

    ⇒ 2b = 12 ⇒ b = 6

    Then a = 3

    Required number = 10 × 6 + 3 = 63

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