In a certain language, if ENTRY is coded as 12345 and STEADY is coded as 931785, then what will be the correct code for the word NEATNESS?

Introduction / Context:
This is a standard letter to digit substitution problem. Each distinct letter has been assigned a unique digit, and the same letter always has the same digit wherever it appears. You must deduce this mapping from the two given words and then apply it to NEATNESS.

Given Data / Assumptions:
ENTRY → 12345.
STEADY → 931785.
We assume that the mapping from letters to digits is one to one and consistent across all words.

Concept / Approach:
Since the same letters appear in both words, we can match their digits and build a table of letter digit pairs. Once the mapping is known for each letter in NEATNESS, we can simply replace letters by digits in order to get the required code.

Step-by-Step Solution:
From ENTRY → 12345, we have E → 1, N → 2, T → 3, R → 4, Y → 5. From STEADY → 931785, we read S → 9, T → 3 (confirming T → 3), E → 1 (confirming E → 1), A → 7, D → 8, Y → 5 (confirming Y → 5). Now we have mappings: A → 7, D → 8, E → 1, N → 2, R → 4, S → 9, T → 3, Y → 5. Write NEATNESS and replace each letter: N E A T N E S S. N → 2, E → 1, A → 7, T → 3, N → 2, E → 1, S → 9, S → 9. Thus NEATNESS becomes 21732199.

Verification / Alternative check:
We can quickly check that every letter in NEATNESS has a mapping derived from the two original words; no new letters appear. Plugging the digits back through the mapping recovers NEATNESS, confirming the correctness of the substitution.

Why Other Options Are Wrong:
Options like 25196577 or 21362199 assign inconsistent digits to letters compared to the mappings we obtained. For example, they may change the digit for N or repeat digits incorrectly. Only 21732199 respects the mapping A → 7, N → 2, E → 1, T → 3 and S → 9 exactly in the right sequence.

Common Pitfalls:
One common error is to misread the second code STEADY and mis-assign digits to letters like A or D. Another is to forget that repeated letters must carry the same digit every time. Writing a clean mapping table and then filling in the target word from left to right prevents such mistakes.

Final Answer:
Therefore, the correct code for NEATNESS is 21732199.