GATE 2025 IN GA Q.7: solution and answer

Official answer: BSource: Official answer key, GATE 2025 IN (IIT Roorkee)

1. Compare the letters position by position first: I→F, M→H, A→B, G→N, E→J. The shifts are $-3,-5,+1,+7,+5$, all different, so the code is not a plain letter shift. The first code letter F is E + 1, and E is the last letter of IMAGE. That suggests the word is reversed first.

2. Reverse IMAGE to get E G A M I, then move each letter one place forward in the alphabet ($+1$): E→F, G→H, A→B, M→N, I→J. This gives FHBNJ, which matches the given code.

3. Check the rule on FIELD. Reversed, it is D L E I F, and $+1$ on each letter gives E M F J G = EMFJG. This also matches, so the rule is: reverse the word, then shift every letter by $+1$.

4. Apply the rule to BEACH. Reversed, it is H C A E B.

5. Shift each letter by $+1$: H→I, C→D, A→B, E→F, B→C. This gives IDBFC, which is option (B).

6. Quick elimination: the code must start with I (H + 1) and end with C (B + 1). Only IDBFC (B) and IBCEC (D) fit. D fails at the second letter, because C + 1 = D, not B.