In a certain code language, the word ACCOUNT is written as DFFRXQW by shifting each letter. Using the same pattern of letter shifts, how is the word MATHS written in that code?

Introduction / Context:
This coding-decoding question is based on a simple letter shift pattern. The word ACCOUNT is transformed into DFFRXQW, and we must discover the rule applied to each letter so that we can encode the new word MATHS in exactly the same way.

Given Data / Assumptions:

• ACCOUNT → DFFRXQW.
• We need to code MATHS using the same transformation rule.
• The alphabet sequence A to Z is assumed to be standard, and wrapping from Z back to A is possible if needed.

Concept / Approach:
We compare each letter in ACCOUNT with the corresponding letter in DFFRXQW to determine how far the alphabet position is shifted. If the shift is consistent, we can apply the same shift to each letter of MATHS. Here, the pattern is a uniform forward shift of three positions in the alphabet for every letter.

Step-by-Step Solution:
Write down the mapping from ACCOUNT to DFFRXQW. A → D, C → F, C → F, O → R, U → X, N → Q, T → W. Check the alphabet positions: A is 1, D is 4, so shift is +3. C (3) to F (6) is also +3, and this continues consistently. Therefore, the rule is: each letter moves three positions forward in the alphabet. Apply this to MATHS. M (13) → P (16), A (1) → D (4), T (20) → W (23), H (8) → K (11), S (19) → V (22). So MATHS becomes PDWKV under this code.

Verification / Alternative check:
We can quickly recheck by reversing: P back by three letters gives M, D back by three gives A, and so on. The decoding correctly reproduces MATHS, which confirms the rule.

Why Other Options Are Wrong:
Options PKLKP, PEWLU and PWDVK correspond to different and inconsistent letter shifts. They do not follow the uniform plus three pattern that transforms ACCOUNT to DFFRXQW. Therefore, they cannot be correct encodings of MATHS in this system.

Common Pitfalls:
Students sometimes look for alternating or irregular shifts when the pattern is actually very simple. Another common error is forgetting that the same rule must apply to all letters of both words; if the rule changes, it is not a valid coding scheme here.

Final Answer:
Using the same letter shift rule, MATHS is coded as PDWKV.