In the following spelling question, four words are given, out of which only one word is correctly spelt. Identify the correct spelling of the word Supernumerary, which refers to something extra or in excess of the normal number.

Introduction / Context:
This question checks your ability to recognise the correct spelling of the word Supernumerary. This formal adjective is often used to describe staff, parts, or items that are more than the usual or required number, such as supernumerary teeth or supernumerary staff. Because the word is somewhat long and has repeated syllables, many learners confuse the placement of vowels and consonants.

Given Data / Assumptions:

• Options: Supernumarary, Supernumerary, Supernumarery, Supernumarey.
• Exactly one option matches the standard spelling used in good dictionaries.
• The other variants contain subtle vowel errors or misplaced letters.
• You must pick the one form that is correct for examinations and formal writing.

Concept / Approach:
The correct spelling is Supernumerary, with the sequence super plus numerary. Think of the root numerical or numerous to notice the same n u m e r pattern. The structure is super numer ary. Any spelling that breaks this numer sequence or changes the final ary ending is incorrect. This method of identifying a known root within a longer word is very useful for remembering tricky spellings, especially in academic English.

Step-by-Step Solution:
Step 1: Break the word into parts: super plus numer plus ary. Step 2: Examine option b, Supernumerary. It clearly keeps the numer root intact and ends with ary. Step 3: Examine option a, Supernumarary. Here, the sequence is numar rather than numer, which is incorrect. Step 4: Examine option c, Supernumarery. This again replaces the e in numer with a and also changes the ending to ery. Step 5: Examine option d, Supernumarey. This not only distorts numer but also gives a non standard ending e y. Step 6: Conclude that Supernumerary is the only form that respects the numer root and matches the known pattern.

Verification / Alternative check:
Recall common usage such as supernumerary police force or supernumerary actors in a play. In each case, the numer part of the word subtly reminds you of number. Checking a standard dictionary entry would show the spelling S U P E R N U M E R A R Y. None of the other options occur in serious texts or official documents. This confirmation through root recognition and dictionary memory ensures that Supernumerary is correct.

Why Other Options Are Wrong:
Supernumarary: Misspells the numer root as numar and so is non standard.
Supernumarery: Contains two errors, both in the central root and in the ending, making it incorrect.
Supernumarey: Changes both internal vowels and final letters, producing a form that does not exist in formal English.

Common Pitfalls:
Many learners are misled by pronunciation and try to write the word exactly as it sounds, which can hide the numer connection. Others focus only on the first part super and neglect the rest. A good strategy is to underline known roots inside long words and to associate them with related words like numeric, numeral, and innumerable. This not only helps you in spelling questions but also strengthens your understanding of word families in English vocabulary.

Final Answer:
The correctly spelt word is Supernumerary, so option b is correct.