In a certain language code, the word TEACHER is written as QBXZEBO by shifting each letter. Using the same coding rule, how will the word STUDENT be written in that code?

Introduction / Context:
This is another letter shifting or Caesar cipher question. The word TEACHER is converted into QBXZEBO using a consistent shift applied to every letter. Once the exact shift is identified, we must apply the same transformation to each letter of the word STUDENT in order to obtain its coded form.

Given Data / Assumptions:

• TEACHER is coded as QBXZEBO.
• The same shifting rule is applied to every letter.
• We need to code the word STUDENT.
• The alphabet positions A = 1 through Z = 26 are used implicitly.
• Shifts wrap around cyclically if they move past A or Z.

Concept / Approach:
We compare each letter in TEACHER with the corresponding letter in QBXZEBO and compute the difference between their positions in the alphabet. If this difference is the same for all pairs, we have found the uniform shift that defines the code. Then we apply this shift to each letter of STUDENT, ensuring we move in the correct direction (forward or backward) and handle wrap around correctly.

Step-by-Step Solution:
Step 1: Determine the positions of the letters in TEACHER: T = 20, E = 5, A = 1, C = 3, H = 8, E = 5, R = 18.Step 2: Determine the positions for the code QBXZEBO: Q = 17, B = 2, X = 24, Z = 26, E = 5, B = 2, O = 15.Step 3: Find the shift for each letter: T (20) to Q (17) is minus 3; E (5) to B (2) is minus 3; A (1) to X (24) is minus 3 with wrap around; C (3) to Z (26) is minus 3; H (8) to E (5) is minus 3; E (5) to B (2) is minus 3; R (18) to O (15) is minus 3.Step 4: The rule is therefore a uniform shift of three letters backward in the alphabet.Step 5: Apply this rule to STUDENT. The positions are S = 19, T = 20, U = 21, D = 4, E = 5, N = 14, T = 20.Step 6: Shift each letter back by three positions: S (19) → P (16), T (20) → Q (17), U (21) → R (18), D (4) → A (1), E (5) → B (2), N (14) → K (11), T (20) → Q (17).Step 7: Combining these letters gives the coded word PQRABKQ.

Verification / Alternative check:
You can reverse check by shifting PQRABKQ three letters forward. P → S, Q → T, R → U, A → D, B → E, K → N and Q → T, which reconstructs STUDENT perfectly. Also, applying the same reverse shift from QBXZEBO to TEACHER confirms that the rule works uniformly both ways.

Why Other Options Are Wrong:
Options such as PQRBAQK, PQRKBAQ, PRKQBAQ and PQRABQK differ in the order of letters or in one or more positions. They do not correspond to a uniform shift of three positions backward from the original word STUDENT. Since the code must follow the exact same Caesar shift rule as TEACHER to QBXZEBO, any deviation from PQRABKQ is incorrect.

Common Pitfalls:
Students may mistakenly apply a forward shift instead of a backward one, or miscount the shift by one position. Another error is to forget the wrap around effect, especially when letters are near the beginning of the alphabet. To avoid mistakes, always compute the numeric positions and subtract or add carefully, checking each letter pair.

Final Answer:
Using the same backward shift of three letters, STUDENT is coded as PQRABKQ.