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    Question

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

    the new number becomes 24 more than 180% of the original number. If the sum of the digits is 6, find the original number.
    A 51 Correct Answer Incorrect Answer
    B 24 Correct Answer Incorrect Answer
    C 15 Correct Answer Incorrect Answer
    D 33 Correct Answer Incorrect Answer
    E 42 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 = (9/5) × (10x + y) + 24

    Multiplying both sides by 5, 
    50y + 5x = 90x + 9y + 120 
    ⇒ 85x − 41y = −120  …. (I)

    And, x + y = 6  …. (II)

    From (II), x = 6 − y. Substitute in (I): 
    85(6 − y) − 41y = −120 
    510 − 126y = −120 
    126y = 630 
    y = 5

    Then x = 1. 
    So, original number = 10 × 1  + 5 = 15.

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