In a two-digit number, if it's unit's digit exceeds it's ten's digit by 2 and that the product of the given number and the sum of digits is equal to 144, then the number is ?
(A) 24
(B) 26
(C) 42
(D) 46
(✓) 24
Lets assume tens digit is x and unit's digit is (x + 2)
(10x + x + 2) (x + x + 2) = 144
(11x + 2)(2x + 2) = 144
22x2 + 26x + 4 = 144
22x2 + 26x - 140 = 0
11x2 + 13x - 70 = 0
(x - 2)(11x + 35) = 0
x = 2
So number is: (10 * 2) + (2 + 2) = 20 + 4 = 24