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    Question

    When the digits of a two-digit number are interchanged,

    the new number becomes 2 more than 200% of the original number. If the sum of the digits is 7, find the original number.
    A 52 Correct Answer Incorrect Answer
    B 34 Correct Answer Incorrect Answer
    C 25 Correct Answer Incorrect Answer
    D 61 Correct Answer Incorrect Answer

    Solution

    Let the unit digit and tens digit of the original number be ‘y’ and ‘x’, respectively.
    Original number = (10x + y)

    According to the data given: 
    10y + x = 2 × (10x + y) + 2 
    10y + x = 20x + 2y + 2 
    ⇒ 19x − 8y = −2  …. (I)

    And, x + y = 7  …. (II)

    From (II), y = 7 − x. Substitute in (I): 
    19x − 8(7 − x) = −2 
    27x = 54 
    x = 2

    Then y = 7 − 2 = 5. 
    So, original number = (10 × 2 + 5) = 25.

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