This question involves a coding language where words are transformed based on a specific pattern. We need to identify this pattern by analysing the given examples and then apply it to the word 'ISOLATION'.

Analyzing the Coding Pattern

Let's examine the first example:

• Original Word: COMMUNITY (9 letters)
• Coded Word: YITUNMCOM

Let's look at the letters and their positions in the original word:

C(1) O(2) M(3) M(4) U(5) N(6) I(7) T(8) Y(9)

The coded word YITUNMCOM appears to rearrange the letters of the original word. Let's try splitting the 9-letter word into three groups of three letters each:

• Group 1 (Letters 1-3): COM
• Group 2 (Letters 4-6): MUN
• Group 3 (Letters 7-9): ITY

Now let's look at the coded word YITUNMCOM and see if it consists of rearrangements of these groups:

• The first three letters of the coded word are YIT. These are the letters from Group 3 (ITY). How are they ordered? Y(9), I(7), T(8). The order is based on their original positions: 9th, 7th, 8th.
• The next three letters are UNM. These are the letters from Group 2 (MUN). How are they ordered? U(5), N(6), M(4). The order is based on their original positions: 5th, 6th, 4th.
• The last three letters are COM. These are the letters from Group 1 (COM). How are they ordered? C(1), O(2), M(3). The order is based on their original positions: 1st, 2nd, 3rd.

So, the pattern for a 9-letter word split into three groups (G1, G2, G3) is that the coded word is formed by rearranging the letters within these groups and combining them in the order G3, G2, G1. The rearrangement within each group is based on the original positions:

• For G3 (letters 7, 8, 9): The order is Position 9, Position 7, Position 8.
• For G2 (letters 4, 5, 6): The order is Position 5, Position 6, Position 4.
• For G1 (letters 1, 2, 3): The order is Position 1, Position 2, Position 3.

Verifying the Pattern with AUTHORITY

Let's check this pattern with the second example:

• Original Word: AUTHORITY (9 letters)
• Coded Word: YITORHAUT

Letters and original positions:

A(1) U(2) T(3) H(4) O(5) R(6) I(7) T(8) Y(9)

Split into groups:

• Group 1 (1-3): AUT
• Group 2 (4-6): HOR
• Group 3 (7-9): ITY

Applying the pattern:

• Coded Group 3 (from ITY - Positions 7, 8, 9): Position 9, Position 7, Position 8 → Y(9) I(7) T(8) → YIT
• Coded Group 2 (from HOR - Positions 4, 5, 6): Position 5, Position 6, Position 4 → O(5) R(6) H(4) → ORH
• Coded Group 1 (from AUT - Positions 1, 2, 3): Position 1, Position 2, Position 3 → A(1) U(2) T(3) → AUT

Combining these gives YITORHAUT, which matches the given coded word for AUTHORITY. The pattern is confirmed.

Applying the Pattern to ISOLATION

Now, let's apply the same pattern to the word ISOLATION.

ISOLATION is a 9-letter word.

Letters and original positions:

I(1) S(2) O(3) L(4) A(5) T(6) I(7) O(8) N(9)

Split into three groups of three letters:

• Group 1 (1-3): ISO (Letters I, S, O)
• Group 2 (4-6): LAT (Letters L, A, T)
• Group 3 (7-9): ION (Letters I, O, N)

Now, apply the reordering rule for each group based on original positions:

• Coded Group 3 (from ION - Positions 7, 8, 9): Position 9, Position 7, Position 8 → N(9) I(7) O(8) → NIO
• Coded Group 2 (from LAT - Positions 4, 5, 6): Position 5, Position 6, Position 4 → A(5) T(6) L(4) → ATL
• Coded Group 1 (from ISO - Positions 1, 2, 3): Position 1, Position 2, Position 3 → I(1) S(2) O(3) → ISO

Combine the coded groups in the order G3, G2, G1:

NIO + ATL + ISO = NIOATLISO

Comparing with Options

The coded word for ISOLATION is NIOATLISO.

Let's check the given options:

1. NIAOTLISO
2. NIOATILSO
3. NIOATLIOS
4. NIOATLISO

The calculated coded word NIOATLISO matches Option 4.

Revision Table: Coding Pattern Summary

Additional Information: Letter Coding and Reasoning

Letter coding is a common type of reasoning question in competitive exams. These questions test your ability to identify hidden patterns or rules governing the transformation of words or letters. The patterns can be varied and might involve:

• Shifting positions of letters (like in this question).
• Assigning numerical values to letters.
• Reversing the entire word or parts of the word.
• Substituting letters with others based on a rule (e.g., opposite letters, letters based on a grid).
• Combining multiple rules.

To solve letter coding problems, it is crucial to:

• Carefully observe the relationship between the original word and the coded word in the given examples.
• Look for patterns in letter positions, sequences, or substitutions.
• If words are split into parts, analyse how the parts are rearranged and how letters within parts are ordered.
• Test the discovered pattern on all given examples to ensure consistency.
• Apply the confirmed pattern to the word you need to code.

This specific problem involved a complex rearrangement based on original letter positions after splitting the word, which is a common technique in such reasoning puzzles.