Step-by-step Solution:

Coding Decoding Problem

Step 1: Analyze the given coding pattern

The word 'ORANGE' is coded as 'MTYPEG'. The relationship between each letter is:

• O (15) → M (13): -2
• R (18) → T (20): +2
• A (1) → Y (25): -2 (A is 1, so going back 2 letters gives Y)
• N (14) → P (16): +2
• G (7) → E (5): -2
• E (5) → G (7): +2

The pattern is a sequence of -2, +2, -2, +2, -2, +2 for each successive letter.

Step 2: Apply the pattern to 'CHILLY'

Apply the pattern to each letter of 'CHILLY':

• C (3) → C - 2 = A (1)
• H (8) → H + 2 = J (10)
• I (9) → I - 2 = G (7)
• L (12) → L + 2 = N (14)
• L (12) → L - 2 = J (10)
• Y (25) → Y + 2 = A (1) (Y is 25, so going forward 2 letters gives A)

Step 3: Combine the coded letters

Combining the coded letters gives AJGNJA.

Answer: The correct option is B. AJGNJA.