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    Question

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

    the new number becomes 39 less than 150% of the original number. If the sum of the digits is 6, find the original number.
    A 24 Correct Answer Incorrect Answer
    B 33 Correct Answer Incorrect Answer
    C 42 Correct Answer Incorrect Answer
    D 51 Correct Answer Incorrect Answer
    E 60 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 = 1.5 × (10x + y) − 39

    Multiplying both sides by 2, 
    20y + 2x = 30x + 3y − 78 
    ⇒ 28x − 17y = 78  …. (I)

    And, x + y = 6  …. (II)

    From (II), x = 6 − y. Substitute in (I): 
    28(6 − y) − 17y = 78 
    168 − 45y = 78 
    45y = 90 
    y = 2

    Then x = 6 − 2 = 4. 
    So, original number = 10 × 4 + 2 = 42.

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