In a two-digit number, 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

=> 22x^2+26x-140=0

=> (x - 2)(11x + 35) = 0

=> x = 2

Hence, Required Number = 11x + 2 = 24

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