Understanding the Coding Language Pattern

The question asks us to decipher a specific code language where 'IMAGE' is encoded as 'KPEJG' and 'HOTEL' is encoded as 'JRXHN'. We need to find the rule behind this encoding and apply it to the word 'JAPAN'.

Analyzing the Encoding Rule

Let's look at the position of each letter in the English alphabet (A=1, B=2, ..., Z=26) and see the difference between the letters in the original words and their encoded forms.

Encoding of 'IMAGE':

• I is the 9th letter, K is the 11th letter. The difference is $\text{11 - 9 = +2}$.
• M is the 13th letter, P is the 16th letter. The difference is $\text{16 - 13 = +3}$.
• A is the 1st letter, E is the 5th letter. The difference is $\text{5 - 1 = +4}$.
• G is the 7th letter, J is the 10th letter. The difference is $\text{10 - 7 = +3}$.
• E is the 5th letter, G is the 7th letter. The difference is $\text{7 - 5 = +2}$.

The sequence of differences is +2, +3, +4, +3, +2.

Encoding of 'HOTEL':

Let's check if the same pattern applies to 'HOTEL'.

• H is the 8th letter, J is the 10th letter. The difference is $\text{10 - 8 = +2}$.
• O is the 15th letter, R is the 18th letter. The difference is $\text{18 - 15 = +3}$.
• T is the 20th letter, X is the 24th letter. The difference is $\text{24 - 20 = +4}$.
• E is the 5th letter, H is the 8th letter. The difference is $\text{8 - 5 = +3}$.
• L is the 12th letter, N is the 14th letter. The difference is $\text{14 - 12 = +2}$.

The sequence of differences is indeed +2, +3, +4, +3, +2. This confirms the pattern for this code language.

Applying the Code to 'JAPAN'

Now, we will apply the discovered pattern (+2, +3, +4, +3, +2) to each letter of the word 'JAPAN'.

Following the pattern, the word 'JAPAN' is encoded as 'LDTDP'.

Revision Table: Code Language Mapping

Here's a summary of the encoding pattern:

• 1st letter: Position + 2
• 2nd letter: Position + 3
• 3rd letter: Position + 4
• 4th letter: Position + 3
• 5th letter: Position + 2

Additional Information on Coding Language Problems

Coding and decoding questions are common in reasoning tests. They often involve patterns based on:

• Letter Shifting: Adding or subtracting a fixed number to the letter's position (like Caesar cipher).
• Patterned Shifting: Adding or subtracting numbers in a specific sequence (as seen in this problem).
• Letter Reversal: Mapping letters from the end of the alphabet to the beginning (A to Z, B to Y, etc.).
• Direct Symbol/Number Substitution: Each letter is replaced by a specific symbol or number.
• Word/Sentence Level Changes: Rearranging words or letters within a word based on a rule.

To solve these problems, it's crucial to write down the alphabet and its positions, compare the given examples, identify the pattern (difference in positions, reversal, etc.), and then apply the same pattern to the word you need to encode or decode.