In a certain code language, the word "ETHANOL" is written as "HWKDQRO". Using the same coding rule, how will the word "MIX" be written in that code language?

Introduction / Context:
This coding decoding problem deals with letter shifts in the English alphabet. One word, ETHANOL, is converted to HWKDQRO. Your goal is to identify the transformation applied to each letter and then use the same rule to encode another word, MIX. These questions are classic examples of alphabet shifting, similar to Caesar ciphers.

Given Data / Assumptions:

• ETHANOL is coded as HWKDQRO.
• The same rule applies to coding MIX.
• All letters are in uppercase and follow standard A to Z ordering.

Concept / Approach:
We compare each letter of ETHANOL with the corresponding letter of HWKDQRO and calculate the shift in alphabetical position. If the shift is constant, we can confidently apply it to other words. In many exam questions, the shift is a small positive number, and letters beyond Z wrap around to the beginning of the alphabet.

Step-by-Step Solution:
Step 1: Write positions: E(5), T(20), H(8), A(1), N(14), O(15), L(12).Step 2: Code positions: H(8), W(23), K(11), D(4), Q(17), R(18), O(15).Step 3: Compute differences: 5 → 8 is +3, 20 → 23 is +3, 8 → 11 is +3, 1 → 4 is +3, 14 → 17 is +3, 15 → 18 is +3, 12 → 15 is +3.Step 4: So the rule is "shift every letter three places forward in the alphabet".Step 5: Apply this to MIX. Positions: M(13), I(9), X(24).Step 6: Add 3: M → P(16), I → L(12), X → 27, which wraps around to A(1).Step 7: Therefore MIX is coded as PLA.

Verification / Alternative check:
We can quickly check that a different constant shift such as +2 or +4 would break at least one letter mapping between ETHANOL and HWKDQRO. The fact that +3 works exactly for every position confirms that we have the correct rule. Applying this rule to MIX gives us PLA without any inconsistencies.

Why Other Options Are Wrong:

• RFV, BGT and NHY would require different non uniform shifts and therefore do not preserve the simple +3 pattern.
• QLA is close but shifts only some letters correctly, meaning the pattern does not match the given example.

Common Pitfalls:
Students sometimes forget to wrap around after Z when shifting forward or mix up the direction of the shift. Another common mistake is checking the rule for only one or two letters instead of confirming it across the entire word. Always verify the pattern for every letter, especially in a code that is supposed to be consistent.

Final Answer:
Using a uniform +3 alphabet shift, MIX is written as PLA in the code language.