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 280, then the number is:

24

35

42

46

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) = 280 => 22x2 + 26x - 276 = 0 => 11x2 + 13x - 138 = 0 => (x - 3)(11x + 46) = 0 => x = 3. Hence, required number = 11x + 2 = 35.

Back To Top