If the word ETHANOL is coded as HWKDQRO using a letter shifting rule, then how will the word MIX be coded?

Introduction / Context:
This is a simple letter coding question. The word ETHANOL is coded as HWKDQRO. You must find the corresponding code for MIX. Most such codes use either a fixed forward or backward shift in the alphabet, or a position based substitution. By comparing ETHANOL and HWKDQRO letter by letter, we can discover the rule and then apply it to MIX.

Given Data / Assumptions:

• Original word: ETHANOL.
• Coded word: HWKDQRO.
• Target word to code: MIX.
• Alphabet positions A 1 to Z 26.
• We assume a consistent shifting rule for all letters in the code.

Concept / Approach:
The natural approach is to compare each letter of ETHANOL with the corresponding letter in HWKDQRO. We convert both sets of letters into their numeric positions and calculate the difference. If the same forward shift appears in every pair, then we apply that shift to the letters of MIX to generate its code. This is essentially a Caesar cipher with a fixed shift.

Step-by-Step Solution:
Step 1: Convert ETHANOL to positions: E 5, T 20, H 8, A 1, N 14, O 15, L 12. Step 2: Convert HWKDQRO to positions: H 8, W 23, K 11, D 4, Q 17, R 18, O 15. Step 3: Compute the differences for each pair: 8 minus 5 equals 3, 23 minus 20 equals 3, 11 minus 8 equals 3, 4 minus 1 equals 3, 17 minus 14 equals 3, 18 minus 15 equals 3, 15 minus 12 equals 3. Step 4: Therefore, each letter is shifted forward by +3 positions in the alphabet to obtain the code. Step 5: Now apply the same rule to MIX. Convert M, I, X to numbers: M 13, I 9, X 24. Step 6: Add 3 to each: 13 plus 3 equals 16, which is P. 9 plus 3 equals 12, which is L. 24 plus 3 equals 27. Since the alphabet has 26 letters, 27 minus 26 equals 1, which is A. Step 7: Combine the shifted letters to get the code: PLA.

Verification / Alternative check:
We can confirm by coding another letter from ETHANOL, for example A. A 1 becomes D 4 when shifted by +3. This matches the third letter in HWKDQRO. Similarly, coding N 14 gives Q 17 and O 15 gives R 18, which fit perfectly. This confirms that the shift is consistent and that our application of +3 to MIX is valid.

Why Other Options Are Wrong:
RFV would correspond to shifts that are not consistently +3 from M, I, X. For example, R is 18, which is 5 ahead of M 13. BGT and NHY similarly require different shifts for different letters, breaking the uniform coding rule. OLA would map from M, I, X using mixed shifts, not the fixed +3 step we discovered.

Common Pitfalls:
Some candidates try to guess the code by visual similarity between ETHANOL and HWKDQRO rather than computing letter positions. Others discover the shift for one letter but do not verify it against all letters, which can lead them to accept the wrong pattern. Always test your inferred rule against every given letter pair before using it on a new word.

Final Answer:
Using the same +3 shift coding as in ETHANOL → HWKDQRO, the correct code for MIX is PLA.