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 280, then the number is:  Select the correct option:
A) 16 B) 24 C) 27 D) 35 E) 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) + (  + 2)= 
<gadget id="calculator">+ (  + 2)</gadget>
<output>2</output>
2x + 2   (11x + 2)(2x + 2)=280   22(x)(x) + 26x - 276 = 0   11(x)(x) + 13x -138 = 0   (x - 3)(11x + 46) = 0   x = 3   Hence, required number = 11x + 2 = 35.   ANSWER:35
<result>D</result>
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 280, then the number is: