Understanding the Coding Logic

The question asks us to find the code for the word 'DUXE' based on the given codes for 'BELO' and 'IGJA'. We need to identify the pattern or rule used in the coding language.

The codes provided are:

• 'BELO' is coded as '271217'
• 'IGJA' is coded as '117103'

Decoding the Pattern

Let's first find the standard alphabetical positions for the letters in the given words:

• A=1, B=2, C=3, ..., Z=26

Now, let's analyze the word 'BELO' and its code '271217':

• B is the 2nd letter.
• E is the 5th letter.
• L is the 12th letter.
• O is the 15th letter.

Comparing the positions (2, 5, 12, 15) with the code (2, 7, 12, 17):

• The code for 'B' (position 2) is '2'.
• The code for 'E' (position 5) is '7'. Notice that $5 + 2 = 7$.
• The code for 'L' (position 12) is '12'.
• The code for 'O' (position 15) is '17'. Notice that $15 + 2 = 17$.

Now, let's analyze the word 'IGJA' and its code '117103':

• I is the 9th letter.
• G is the 7th letter.
• J is the 10th letter.
• A is the 1st letter.

Comparing the positions (9, 7, 10, 1) with the code (11, 7, 10, 3):

• The code for 'I' (position 9) is '11'. Notice that $9 + 2 = 11$.
• The code for 'G' (position 7) is '7'.
• The code for 'J' (position 10) is '10'.
• The code for 'A' (position 1) is '3'. Notice that $1 + 2 = 3$.

From these observations, we can infer a pattern:

• Letters B, L, G, J did not change their position values in the code. These are consonants.
• Letters E, O, I, A had 2 added to their position values. These are vowels.

The Rule: Vowels are coded by adding 2 to their alphabetical position, while consonants are coded using their standard alphabetical position. The results are then concatenated.

Applying the Rule to 'DUXE'

Let's find the alphabetical positions for the letters in 'DUXE':

• D is the 4th letter.
• U is the 21st letter.
• X is the 24th letter.
• E is the 5th letter.

Now, apply the coding rule:

• D: Consonant, position 4. Code is 4.
• U: Vowel, position 21. Code is $21 + 2 = 23$.
• X: Consonant, position 24. Code is 24.
• E: Vowel, position 5. Code is $5 + 2 = 7$.

Concatenate the results: 4, 23, 24, 7 gives '423247'.

Final Coded Word

Therefore, 'DUXE' will be coded as '423247'.