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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:

Correct Answer: 24

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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