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    Question

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

    the new number becomes 11 more than 120% of the original number. If the sum of the digits is 8, find the original number.
    A 53 Correct Answer Incorrect Answer
    B 44 Correct Answer Incorrect Answer
    C 35 Correct Answer Incorrect Answer
    D 62 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 = 1.2 × (10x + y) + 11

    Multiplying both sides by 5, 
    50y + 5x = 60x + 6y + 55 
    ⇒ 55x − 44y = −55  …. (I)

    And, x + y = 8  …. (II)

    From (II), x = 8 − y. Substitute in (I): 
    55(8 − y) − 44y = −55 
    440 − 99y = −55 
    99y = 495 
    y = 5

    Then x = 8 − 5 = 3. 
    So, original number = (10 × 3 + 5) = 35.

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