In a certain code language, the word FIR is written as 33 and the word LIT is written as 41. Using the same letter value pattern, how is the word TOM written in that code?

Introduction / Context:
This problem belongs to the category where words are coded as numbers based on alphabet positions. We are told that FIR corresponds to 33 and LIT corresponds to 41, and we must determine the numerical code for TOM. Typically, such questions involve summing the positions of letters in the alphabet, and sometimes additional operations like multiplication or adding constants.

Given Data / Assumptions:

• The word FIR is coded as the number 33.
• The word LIT is coded as the number 41.
• We must find the code for TOM using the same logic.
• Alphabet positions are taken as A = 1, B = 2, and so on up to Z = 26.
• No extra symbols or operations beyond simple arithmetic are suggested.

Concept / Approach:
We begin by checking whether the code number equals the sum of the positions of the letters in each word. For FIR, we compute F plus I plus R and compare the result with 33. If the sum matches, the pattern is likely the simple sum of positions. We confirm this with the second example LIT before applying the same rule to TOM. This approach is straightforward and common in spelling to number coding questions.

Step-by-Step Solution:
Step 1: Determine the positions of the letters in FIR. F is the 6th letter, I is the 9th, and R is the 18th.Step 2: Sum these values: 6 + 9 + 18 = 33, which matches the given code for FIR.Step 3: Check the second example LIT. L is 12, I is 9, and T is 20.Step 4: Sum them: 12 + 9 + 20 = 41, which matches the given code for LIT.Step 5: Conclude that the rule is simply the sum of alphabet positions of the letters.Step 6: Now find the positions of T, O, and M in TOM. T is 20, O is 15, and M is 13.Step 7: Sum them: 20 + 15 + 13 = 48.

Verification / Alternative check:
To verify the consistency of the rule, we could test another word built from the same letters, such as FIT, and check that its code would be 6 + 9 + 20 = 35. The pattern of summing letter positions is stable and unique for a given word. Since the pattern matches both examples FIR and LIT and yields a clear value for TOM, there is no need for more complicated interpretations. The answer 48 fits perfectly with all observations.

Why Other Options Are Wrong:
The numbers 39, 40, 46, and 52 do not equal the sum of the positions of T, O, and M. Any answer other than 48 would require a different rule that does not simultaneously match both given examples. For instance, 46 would correspond to subtracting two from the correct sum, which has no justification in the data. Therefore these values are included only as distractors for candidates who compute the sum incorrectly.

Common Pitfalls:
Students sometimes miscount alphabet positions, especially for letters near the end of the alphabet, or they skip one letter while counting. Another mistake is to assume products or more complex operations before testing simple addition. Writing down the alphabet with position numbers or recalling well known positions like 1, 5, 10, 20 helps avoid errors. Always verify the rule with every example provided before applying it to the target word.

Final Answer:
Using the rule that each word is coded as the sum of the positions of its letters, the word TOM is coded as 48.