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  1. In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
    2. A.

    24
    B.

    26
    C.

    42
    D.

    46

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    Answer : Option A

    Explanation :

    Let the ten's digit be x.

     

    Then, unit's digit = x + 2.

     

    Number = 10x + (x + 2) = 11x + 2.

     

    Sum of digits = x + (x + 2) = 2x + 2.

     

     (11x + 2)(2x + 2) = 144

     

     22x2 + 26x - 140 = 0

     

     11x2 + 13x - 70 = 0

     

     (x - 2)(11x + 35) = 0

     

     x = 2.

     

    Hence, required number = 11x + 2 = 24.

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