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Problems on Numbers - General Aptitude

Q1:

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:

A 24

B 26

C 42

D 46

ANS:A - 24

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.