In the following letter analogy question, select the group of letters from the alternatives that best completes the analogy BDGK : ACFJ :: ? : DFIM.

Introduction / Context:
This analogy problem tests understanding of alphabetical letter positions and consistent patterns between two pairs of letter groups. Such questions are common in aptitude and reasoning exams, where the goal is to identify a hidden rule in the first pair and then apply the same rule to find the missing term in the second pair.

Given Data / Assumptions:
We are given the pair BDGK : ACFJ. We must relate an unknown group of letters ? to DFIM in the same way. All letters are from the English alphabet and the pattern is assumed to be purely positional. The answer must be chosen from the provided options.

Concept / Approach:
The main idea is to convert each letter into its numerical position in the alphabet and then look for a consistent transformation. Once the relation between BDGK and ACFJ is understood, the same transformation is applied in reverse to generate the missing group that should correspond to DFIM. Letter analogy questions often use operations like addition, subtraction, or mirror positions in the alphabet, but in this case the pattern is a simple shift of one position backward for each letter.

Step-by-Step Solution:
Step 1: Write the letter positions for BDGK. B = 2, D = 4, G = 7, K = 11. Step 2: Write the letter positions for ACFJ. A = 1, C = 3, F = 6, J = 10. Step 3: Compare corresponding positions. 2 to 1 is -1, 4 to 3 is -1, 7 to 6 is -1, 11 to 10 is -1. So, each letter in BDGK is shifted one step back in the alphabet to obtain ACFJ. Step 4: The same relation must hold in the second pair. Unknown group ? when shifted one step back for each letter must give DFIM. Step 5: Reverse the transformation by shifting each letter in DFIM one step forward. D (4) + 1 = E (5). F (6) + 1 = G (7). I (9) + 1 = J (10). M (13) + 1 = N (14). Therefore the required group is EGJN.

Verification / Alternative check:
We can verify by now applying the discovered rule again. Starting from EGJN, move each letter one step back: E to D, G to F, J to I, N to M. This gives DFIM, which exactly matches the second group given in the question. The pattern is therefore consistent with the first pair and validated for the second pair as well.

Why Other Options Are Wrong:
FKLO gives EJLN when each letter is moved one step back, which does not match DFIM. CEHK gives BDGJ when shifted back, which is not DFIM. FHJM gives EGIL when shifted back, which does not match DFIM. DHJL gives CGIK when shifted back, which again is different from DFIM.

Common Pitfalls:
Many learners focus only on the differences within each group (for example, the gaps between letters inside BDGK and ACFJ) and ignore the direct letter to letter relationship across the colon. Others may incorrectly apply additions instead of subtractions or mix up the direction of the shift. It is important to always work systematically from the first pair, identify a precise transformation, and then apply that same rule consistently to the second pair. Ignoring the exact letter positions or making assumptions without checking each letter can lead to incorrect choices.

Final Answer:
The group of letters that maintains the same relationship is EGJN.