To solve this question, we need to identify the pattern or rule used to convert the given words into the corresponding code.

1. Analyzing the word "GRAPE":
- The word "GRAPE" is converted into the code "27354".
- We can observe that each letter in the word is replaced with a unique digit.
- Therefore, the code is based on a substitution cipher, where each letter is replaced by a specific digit.

2. Analyzing the word "FOUR":
- The word "FOUR" is converted into the code "1687".
- Applying the same pattern as observed in "GRAPE," we can deduce that each letter is replaced by a digit.

3. Identifying the pattern:
- To determine the specific digit assigned to each letter, we can compare the positions of the letters in the alphabet with their corresponding digits in the code.
- The position of "G" in the alphabet is 7, and it corresponds to the first digit in the code, which is 2.
- The position of "R" is 18, and it corresponds to the second digit, which is 7.
- The position of "A" is 1, and it corresponds to the third digit, which is 3.
- The position of "P" is 16, and it corresponds to the fourth digit, which is 5.
- The position of "E" is 5, and it corresponds to the fifth digit, which is 4.

4. Applying the pattern to the word "GROUP":
- The position of "G" is 7, so it corresponds to the first digit in the code.
- The position of "R" is 18, so it corresponds to the second digit.
- The position of "O" is 15, so it corresponds to the third digit.
- The position of "U" is 21, so it corresponds to the fourth digit.
- The position of "P" is 16, so it corresponds to the fifth digit.

Therefore, the code for the word "GROUP" is "27685", which is option C.