Step 1: Understanding the Question:
This is a coding-decoding problem where we need to find the transformation logic applied to the word "MANGO" and apply the same to "ORANGE".
Step 2: Detailed Explanation:
Cracking the code for MANGO: Let's look at the alphabetical positions of the letters.
M (13) $\rightarrow$ R (18) : (+5)
A (1) $\rightarrow$ F (6) : (+5)
N (14) $\rightarrow$ S (19) : (+5)
G (7) $\rightarrow$ L (12) : (+5)
O (15) $\rightarrow$ T (20) : (+5)
The logic is simply adding 5 to the position of each letter in the alphabet.
Applying logic to ORANGE:
O (15) + 5 = 20 $\rightarrow$ T
R (18) + 5 = 23 $\rightarrow$ W
A (1) + 5 = 6 $\rightarrow$ F
N (14) + 5 = 19 $\rightarrow$ S
G (7) + 5 = 12 $\rightarrow$ L
E (5) + 5 = 10 $\rightarrow$ J
Step 3: Final Answer:
The word "ORANGE" coded with a +5 shift becomes "TWFSLJ". This corresponds to option (E).