In a certain code language CARPET is written as FDUSHW. How will MOTHER be…

In alphabet letter-coding questions, every letter of a word is shifted a fixed number of positions along the alphabet (a Caesar-cipher-style substitution) to produce its code. The shift amount stays constant for the whole word and is found by comparing one given plaintext-to-code pair before being applied to any other word in the same code.

1. Compare each letter of CARPET with its coded letter in FDUSHW: C→F, A→D, R→U, P→S, E→H, T→W.

2. Each letter moves forward by exactly 3 positions in the alphabet (C+3=F, A+3=D, R+3=U, P+3=S, E+3=H, T+3=W), confirming a constant +3 shift.

3. Apply the same +3 shift to every letter of MOTHER, in order: M+3=P, O+3=R, T+3=W, H+3=K, E+3=H, R+3=U.

4. Read the shifted letters in the original word's order to get the coded word: P, R, W, K, H, U.

Cross-check by reversing the shift: subtracting 3 from each letter of the result (P-3=M, R-3=O, W-3=T, K-3=H, H-3=E, U-3=R) exactly reconstructs MOTHER, confirming the +3 rule works in both directions.

Applying the code language's +3 forward-shift rule, MOTHER is coded as PRWKHU.