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    Question

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

    the new number becomes 19 less than 150% of the original number. If the sum of the digits is 11, find the original number.
    A 65 Correct Answer Incorrect Answer
    B 56 Correct Answer Incorrect Answer
    C 47 Correct Answer Incorrect Answer
    D 38 Correct Answer Incorrect Answer
    E 29 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) − 19
    Multiplying both sides by 2, 
    20y + 2x = 30x + 3y − 38 
    ⇒ 28x − 17y = 38  …. (I)
    And, x + y = 11  …. (II)
    From (II), x = 11 − y. Substitute in (I): 
    28(11 − y) − 17y = 38 
    308 − 45y = 38 
    45y = 270 
    y = 6
    Then x = 5. 
    So, original number = 10 × 5 + 6 = 56.

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