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    Question

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

    the new number becomes 18 more than 125% of the original number. If the sum of the digits is 9, find the original number.
    A 72 Correct Answer Incorrect Answer
    B 54 Correct Answer Incorrect Answer
    C 36 Correct Answer Incorrect Answer
    D 63 Correct Answer Incorrect Answer
    E 27 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 = 1.25 × (10x + y) + 18

    Multiplying both sides by 4, 
    40y + 4x = 50x + 5y + 72 
    ⇒ 46x − 35y = −72  …. (I)

    And, x + y = 9  …. (II)

    From (II), x = 9 − y. Substitute in (I): 
    46(9 − y) − 35y = −72 
    414 − 81y = −72 
    81y = 486 
    y = 6

    Then x = 9 − 6 = 3. 
    So, original number = (10 × 3 + 6) = 36.

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