In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 3 and that the product of the given number and the sum of its digits is equal to 324, then the number is:
Options:
A) 12
B) 14
C) 23
D) 25
E) 36
Let the ten's digit be x. Then, unit's digit = x + 3. Number = 10x + (x + 3) = 11x + 3   Sum of digits = x + (x + 3) = 2x + 3   (11x + 3)(2x + 3) = 324   22(x)(x) + 39x - 315 = 0   (x - 3)(22x + 105) = 0   x = 3   Hence, required number = 11x + 3 = 36.   ANSW36R:36
<result>E</result>
In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 3 and that the product of the given number and the sum of its digits is equal to 324, then the number is: