Question

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:

Answer 1

Let the ten's digit be x.

and the unit's digit be x + 2.

Let the required number be 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.