Multiple choice

In a two-digit number, its unit's digit exceeds its ten's digit by 2 and the product of the given number and the sum of its digits is equal to 144, then the number is

  1. 24

  2. 26

  3. 42

  4. 46

  5. None of these
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A Correct answer
Explanation

Let the ten's digit be x. Then, unit's digit will be x + 2. The number = 10x + (x + 2) = 11x + 2 The 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, the required number = 11x + 2 = 24

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