In a certain code language, the word "PROBLEM" is written as MPERLOB. In the same code, how will the word "NUMBERS" be written?

Introduction / Context:
Here, the letters of a word are rearranged according to a fixed positional pattern that turns PROBLEM into MPERLOB. You have to discover that positional rearrangement and apply it to NUMBERS. This is a typical pattern recognition question in coding decoding.

Given Data / Assumptions:
Original word: PROBLEM (1 P, 2 R, 3 O, 4 B, 5 L, 6 E, 7 M).
Coded word: MPERLOB.
We need to code NUMBERS, another seven letter word. We assume the mapping is purely positional and the same for all seven letter words.

Concept / Approach:
The strategy is to see from which positions in PROBLEM each letter in MPERLOB comes. That gives us a positional permutation. Once we know this order, we can apply the same positional permutation to NUMBERS to get its code.

Step-by-Step Solution:
Write the letters of PROBLEM with their positions: 1 P, 2 R, 3 O, 4 B, 5 L, 6 E, 7 M. The code MPERLOB has letters: M, P, E, R, L, O, B. Match each coded letter to its original position: M comes from position 7, P from 1, E from 6, R from 2, L from 5, O from 3, and B from 4. Thus the new order of positions is [7, 1, 6, 2, 5, 3, 4]. Now write NUMBERS with positions: 1 N, 2 U, 3 M, 4 B, 5 E, 6 R, 7 S. Apply the same position order 7, 1, 6, 2, 5, 3, 4: 7→S, 1→N, 6→R, 2→U, 5→E, 3→M, 4→B, giving SNRUEMB.

Verification / Alternative check:
We can verify by reversing the permutation. If we take SNRUEMB and apply the inverse positional mapping, we should get NUMBERS. Doing so restores each letter to its original position, confirming that we have used the same transformation as in PROBLEM → MPERLOB.

Why Other Options Are Wrong:
SNUREMB, SNRUBME and SNRUMEB all differ in the relative arrangement of the letters U, E and M. None of these can be generated by the exact positional order [7, 1, 6, 2, 5, 3, 4] that we derived from the given example. Therefore they do not correctly follow the coding rule.

Common Pitfalls:
Students sometimes guess that the first and last letters are merely swapped or that the word is reversed and then slightly altered. Without explicitly tracking positions, it is easy to miss the true permutation. Always write indices and track where each letter moves when a word is coded.

Final Answer:
Using the same positional rearrangement, the word NUMBERS is written as SNRUEMB.