In a certain code language, 'BELO' is coded as '271217' and 'IGJA' is coded as '117103'. How will 'DUXE' be coded in that language?

Let's check the positional numbers of the letters in 'BELO':
B = 2

E = 5

L = 12

O = 15

Now let's look at the code: 271217
Break it down relative to the letters:

B → 2

E → 7 (which is 5+2)

L → 12

O → 17 (which is 15+2)

So the pattern is: Odd positions keep their direct positional value, even positions add 2 to their value.

Let's verify with IGJA → 117103:

I (1st, 9) → 9? Wait, the code starts with 11. Let's see:

If I (9) +2=11

G (2nd, 7) → 7

J (3rd, 10) → 10

A (4th, 1) +2=3
Ah! Let's check Vowels vs Consonants:
In BELO:

B (Consonant) = 2

E (Vowel) = 5+2=7

L (Consonant) = 12

O (Vowel) = 15+2=17
Code: 2 7 12 17 → 271217.

In IGJA:

I (Vowel) = 9+2=11

G (Consonant) = 7

J (Consonant) = 10

A (Vowel) = 1+2=3
Code: 11 7 10 3 → 117103.

So the logic is: Consonants = direct positional value, Vowels = positional value + 2.

Now let's apply this to DUXE:

D (Consonant) = 4

U (Vowel) = 21+2=23

X (Consonant) = 24

E (Vowel) = 5+2=7

Combining them: 423247.