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    Question

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

    the new number becomes 23 more than 150% of the original number. If the sum of the digits is 8, find the original number.
    A 62 Correct Answer Incorrect Answer
    B 44 Correct Answer Incorrect Answer
    C 26 Correct Answer Incorrect Answer
    D 35 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) + 23
    Multiplying both sides by 2, 
    20y + 2x = 30x + 3y + 46 
    ⇒ 28x − 17y = −46  …. (I)
    And, x + y = 8  …. (II)
    From (II), x = 8 − y. Substitute in (I): 
    28(8 − y) − 17y = −46 
    224 − 45y = −46 
    45y = 270 
    y = 6
    Then x = 2. 
    So, original number = 10 × 2 + 6 = 26.

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