The sum of two numbers is 216 and their H.C.F. is 27. The numbers are · ABC26GN0484

Let the required numbers be $27 a$ and $27 b$. Then, $27 a+27 b=216 \Rightarrow a+b=8$. Now, co-primes with sum 8 are $(1,7)$ and $(3,5)$. ∴ Required numbers are (27 × 1, 27 × 7) and (27 × 3, $27 \times 5)$ i.e., $(27,189)$ and $(81,135)$. Out of these, the one available in the given alternatives is the pair (27, 189).