In a certain code language, the word FASHION is coded as FOIHSAN by rearranging its letters. Using the same coding pattern, how is the word PROBLEM coded in that language?

Introduction / Context:
This verbal reasoning question is from the coding–decoding topic. Instead of replacing letters with numbers, the code rearranges the letters of the word FASHION to obtain FOIHSAN. Our job is to carefully observe the pattern used in this rearrangement and then apply exactly the same pattern to a new word, PROBLEM, so that we can find its correct coded form from the given options.

Given Data / Assumptions:

• FASHION is written as FOIHSAN in the secret code.
• We must use the same coding pattern for the word PROBLEM.
• No letters are added or removed; only their order changes.
• Each letter in the original word appears exactly once in the coded word.

Concept / Approach:
The key idea is to map each position of the original word to a specific position in the coded word. We compare FASHION and FOIHSAN letter by letter. By aligning positions, we can see how the first, second, third and so on letters are rearranged. Once this positional pattern is clear, we will apply the same order of positions to the word PROBLEM. This approach avoids guessing and guarantees the correct answer if we follow the mapping correctly.

Step-by-Step Solution:
Step 1: Write FASHION with its positions: 1-F, 2-A, 3-S, 4-H, 5-I, 6-O, 7-N. Step 2: Write FOIHSAN with positions: 1-F, 2-O, 3-I, 4-H, 5-S, 6-A, 7-N. Step 3: Observe the mapping: position 1 stays 1, position 6 becomes 2, position 5 becomes 3, position 4 stays 4, position 3 becomes 5, position 2 becomes 6 and position 7 stays 7. Step 4: Express this as a pattern of positions: [1, 6, 5, 4, 3, 2, 7]. Step 5: Now apply this to PROBLEM (1-P, 2-R, 3-O, 4-B, 5-L, 6-E, 7-M). Using the same order we get: 1 -> P, 6 -> E, 5 -> L, 4 -> B, 3 -> O, 2 -> R, 7 -> M, which forms PELBORM.

Verification / Alternative check:
We can quickly check that PELBORM uses every letter of PROBLEM exactly once and that the positional rule corresponds perfectly to what was done for FASHION. No other option follows the same consistent positional pattern [1, 6, 5, 4, 3, 2, 7] when applied to PROBLEM, so the code PELBORM is unique and correct.

Why Other Options Are Wrong:
Option B: PRBOELM rearranges the letters in a different order and does not follow the [1, 6, 5, 4, 3, 2, 7] pattern. Option C: RPBOELM starts with R instead of P, which already violates the first position rule. Option D: PELBMOR changes the relative positions of B, M, O and R compared to the required mapping. Option E: PROBELM is only a mild shuffle of the original word, not the specific coded pattern derived from FASHION.

Common Pitfalls:
Many test-takers try to guess the answer by visual similarity or by counting letters without analysing the exact positions. Another common mistake is to look for shifts in alphabet order rather than noticing that this question is about rearrangement only. Some students also miscopy positions or accidentally skip a letter when applying the pattern, which leads to near-miss options that look almost correct but are wrong. Carefully writing down positions and applying the pattern systematically avoids these errors.

Final Answer:
The word PROBLEM is coded as PELBORM in this language.