In the following question, select the related group of letters from the given alternatives: FUT is to JYX as BUG is to which group?

Introduction / Context:
This analogy is a standard alphabet shift coding problem. The group FUT is coded as JYX, and you must determine the coded form of BUG using the same rule. Identifying the exact alphabetic shift between corresponding letters and applying it consistently to a new group is central to solving this type of question.

Given Data / Assumptions:

• The example coding is FUT on the left mapped to JYX on the right.
• The second original group is BUG, whose code we must find.
• The options are AYG, FYK, LCK, and FAM.
• We work with alphabet positions A = 1 through Z = 26.
• We assume the same shift is applied to all three letters of FUT to obtain JYX.

Concept / Approach:
First, convert the letters in FUT and JYX to their numeric positions and calculate the difference. If every letter in FUT shifts by the same amount to become the corresponding letter in JYX, then that constant shift is the coding rule. We then apply that rule to each letter in BUG and see which answer option matches the resulting letters. This constant shift approach is typical in three letter coding analogies.

Step-by-Step Solution:
Step 1: Write the positions of FUT. F is 6, U is 21, and T is 20. Step 2: Write the positions of JYX. J is 10, Y is 25, and X is 24. Step 3: Compute the shift for each letter: from F(6) to J(10) is +4; from U(21) to Y(25) is +4; from T(20) to X(24) is +4. Step 4: Conclude that the coding rule is to add 4 to each letter's position. Step 5: Now apply this rule to BUG. B is 2, U is 21, and G is 7. Step 6: Add 4: B(2) + 4 = 6 (F); U(21) + 4 = 25 (Y); G(7) + 4 = 11 (K). Step 7: Combine the letters F, Y, and K to obtain FYK, which matches option b.

Verification / Alternative check:
To verify, we can decode JYX back to FUT by subtracting 4 from each letter. J(10) minus 4 is 6 (F), Y(25) minus 4 is 21 (U), and X(24) minus 4 is 20 (T). This confirms the rule is consistent and reversible. Trying the same +4 shift on BUG leads uniquely to FYK, and no other option corresponds to a constant +4 shift, which confirms FYK as the correct coded group.

Why Other Options Are Wrong:
AYG, LCK, and FAM do not result from adding 4 to each letter in BUG. For example, to move from B to A would require a shift of minus 1, not plus 4. To get from U to Y is plus 4, but combining inconsistent shifts would break the pattern established by FUT : JYX. Since the essence of the example is a uniform +4 shift, any option that does not conform to this rule must be discarded.

Common Pitfalls:
A common error is to overlook the modular nature of the alphabet when shifting near the end and beginning (around X, Y, Z, A), but in this case the shifts stay well within bounds, making the pattern easy to confirm. Another pitfall is to miscalculate letter positions under exam stress. Writing down a quick A to Z position reference or keeping mental track carefully helps avoid such mistakes.

Final Answer:
Using the same +4 alphabet shift that converts FUT to JYX, the group BUG is coded as FYK.