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    Question

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

    the new number becomes 5 less than 150% of the original number. If the sum of the digits is 10, find the original number.
    A 64 Correct Answer Incorrect Answer
    B 46 Correct Answer Incorrect Answer
    C 56 Correct Answer Incorrect Answer
    D 73 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) − 5

    Multiplying both sides by 2, 
    20y + 2x = 30x + 3y − 10 
    ⇒ 28x − 17y = 10  …. (I)

    And, x + y = 10  …. (II)

    From (II), x = 10 − y. Substitute in (I): 
    28(10 − y) − 17y = 10 
    280 − 45y = 10 
    45y = 270 
    y = 6

    Then x = 10 − 6 = 4. 
    So, original number = (10×4 + 6) = 46.

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