The correct option is B 13,14
Let one number be x
Thus, the other number is 27−x
Now, x(27−x)=182
⇒27x−x2−182=0
⇒x2−27x+182=0
⇒x2−14x−13x+182=0
⇒x(x−14)−13(x−14)=0
⇒(x−14)(x−13)=0
Thus, x−14=0 or x−13=0
⇒x=14 or x=13
⇒27−x=27−14=13 or 27−x=27−13=14
Therefore, the required numbers are 13,14.