If in a certain code language the word "TEACHER" is written as "VGCEJGT", how would the word "STUDENT" be written in the same code?

Introduction / Context:
Here we have a simple alphabet shifting code. Each letter in the original word TEACHER is moved forward in the alphabet to create the coded word VGCEJGT. We need to detect the constant shift used and then apply it consistently to all letters of the word STUDENT. This type of code is essentially a Caesar cipher and is very common in coding decoding questions.

Given Data / Assumptions:

• "TEACHER" is written as "VGCEJGT".
• We must find the coded form of "STUDENT".
• The order of letters is preserved and each letter is shifted by the same number of positions.

Concept / Approach:
To identify the rule, compare corresponding letters in TEACHER and VGCEJGT. If each letter in the coded word is a fixed number of positions ahead of the original, then the code is a uniform shift cipher. Once we determine the number of positions, we apply the same forward shift to each letter in STUDENT to obtain the coded word.

Step-by-Step Solution:
Step 1: Compare T with V. T is the 20th letter, V is the 22nd, so this is a shift of plus two positions. Step 2: Check other letters to confirm: E goes to G (5 to 7), A goes to C (1 to 3), C goes to E (3 to 5), H goes to J (8 to 10), E goes to G again and R goes to T (18 to 20). All shifts are plus two. Step 3: Conclude that the rule is to move each letter forward by two positions in the alphabet, wrapping around if necessary. Step 4: Now apply this to STUDENT. Write down S, T, U, D, E, N and T. Step 5: Shift S (19) forward by two positions to U (21). Step 6: Shift T (20) forward by two positions to V (22). Step 7: Shift U (21) forward by two positions to W (23). Step 8: Shift D (4) forward by two positions to F (6). Step 9: Shift E (5) forward by two positions to G (7). Step 10: Shift N (14) forward by two positions to P (16). Step 11: Finally, shift T (20) forward by two positions to V (22). Step 12: Putting these together gives U W V F G P V, written as UWVFGPV.

Verification / Alternative check:
We can verify by reversing the shift. If we take UWVFGPV and shift each letter backward by two positions, we should recover STUDENT. U back two is S, W back two is U, V back two is T, F back two is D, G back two is E, P back two is N and V back two is T. This confirms that the forward shift of two is applied consistently and correctly.

Why Other Options Are Wrong:
The alternative options swap some letters or apply the shift incorrectly. For example, UWVGFPV changes the order of F and G, which is not supported by a simple uniform shift. Similarly, UVWFGPV and UVWFPGV do not match the exact sequence produced by shifting each original letter forward by two positions. Therefore they cannot arise from the given coding rule.

Common Pitfalls:
A common mistake is to miscount the positions when shifting letters or to assume a different shift for vowels and consonants. Another error is to reverse the direction of the shift, moving letters backward instead of forward. Carefully checking a couple of letter pairs is usually enough to fix the direction and magnitude of the shift.

Final Answer:
Using the same plus two shift that maps TEACHER to VGCEJGT, the word "STUDENT" is written as UWVFGPV.