In the following pair analogy, FED is related to IHG. Using the same pattern, which of the following pairs of letters correctly completes the analogy ? : ?

Introduction / Context:
This question tests understanding of letter based analogies involving a constant shift in alphabet positions. The pair FED and IHG shows how each letter of the first group changes to produce the second group. We must identify another pair from the options that follows the same rule. Such problems are common in reasoning tests and help develop quick mental mapping between letters and their positions.

Given Data / Assumptions:

• Given pair: FED : IHG
• We must find another pair X : Y from the options that shows the same relationship.
• Options include different pairs of three letter groups.
• We use English alphabet positions from A equal to 1 to Z equal to 26.

Concept / Approach:
The natural approach is to convert letters to their numeric positions, compute the difference from each letter in the first group to the corresponding letter in the second group, and see whether the difference is the same. If the difference is constant for all letters, we have found the transformation rule. Then we will scan the options to find another pair where the second group is obtained by applying the same numeric shift to the first group.

Step-by-Step Solution:
Step 1: Write positions for FED. F is 6, E is 5, D is 4. Step 2: Write positions for IHG. I is 9, H is 8, G is 7. Step 3: Compute the differences. From F (6) to I (9) the change is plus 3. From E (5) to H (8) the change is plus 3. From D (4) to G (7) the change is also plus 3. Step 4: Conclude that the rule is "add 3 positions" to each letter of the first group to obtain the second group. Step 5: Check option TSR : WVU. Positions for TSR are T equal to 20, S equal to 19, R equal to 18. Positions for WVU are W equal to 23, V equal to 22, U equal to 21. The changes are 20 to 23 plus 3, 19 to 22 plus 3, and 18 to 21 plus 3. So this option perfectly follows the same rule.

Verification / Alternative check:
Verify other options quickly. For ACB : GUV, A to G is plus 6, C to U is plus 18, B to V is plus 20, so the shift is not constant. For VUK : LMO, V to L requires wrapping and does not give a consistent plus 3 across all letters. For DEF : IGH, D to I is plus 5, E to G is plus 2, and F to H is plus 2, so again the changes do not match the required plus 3. Only TSR : WVU shows a uniform addition of 3 for every letter, which is required for a valid analogous pair.

Why Other Options Are Wrong:
Each incorrect option fails because the difference between first and second group letters is not the same across all three positions. Either the shift varies or some letters require wrapping around the alphabet in inconsistent ways. Since the original pair clearly uses the simple rule of adding three to every letter, any deviation from this rule breaks the analogy and makes the option invalid.

Common Pitfalls:
Examinees sometimes glance quickly and see that the letters in the second group look similar or close to those in the first group and then guess without calculating exact differences. This habit leads to picking options where the shift is mixed. To avoid this, always compute numeric positions and verify that the same operation works for every letter. A systematic method, even for simple looking questions, prevents careless errors.

Final Answer:
The pair of letters that correctly completes the analogy FED : IHG :: ? : ? is TSR : WVU.