In a certain code language, words are converted into numbers using a specific hidden pattern. For example, the word GOAT is written as 45 and the word COAT is written as 41 in this code. Using the same rule, what numerical code should represent the word BOAT ?

Introduction / Context:
This is a classic coding and decoding question in verbal reasoning, where English words are converted into numbers according to a simple but hidden rule. We are told how GOAT and COAT are coded, and we must use that information to determine the code for BOAT. The challenge is to recognise the connection between the letters of each word and the resulting number without overcomplicating the pattern. Such questions are common in aptitude exams because they check basic familiarity with alphabetical positions and logical pattern deduction.

Given Data / Assumptions:

• The word GOAT is coded as the number 45.
• The word COAT is coded as the number 41.
• The same coding rule is used consistently for all words in this question.
• The target word is BOAT and we must find its numerical code.
• We assume standard English alphabetical positions, where A = 1, B = 2, C = 3, and so on.

Concept / Approach:
In letter to number coding, a very common approach is to use the sum of the alphabetical positions of the letters. If that sum does not directly match the given code, we usually try adding or subtracting a small constant. So we first compute the sum of the positions of G, O, A, T and compare it with 45. Then we do the same for C, O, A, T and compare with 41. If the same simple adjustment works for both examples, we adopt that as the rule and then apply it to BOAT in a systematic way.

Step-by-Step Solution:
Step 1: Find the alphabetical positions of each letter in GOAT: G = 7, O = 15, A = 1, T = 20. Step 2: Sum these positions: 7 + 15 + 1 + 20 = 43. Step 3: The code given for GOAT is 45, which is 43 + 2. Step 4: Now check COAT. Positions are C = 3, O = 15, A = 1, T = 20. Step 5: Sum for COAT is 3 + 15 + 1 + 20 = 39. The code is 41, which is 39 + 2. Step 6: The same rule appears in both cases, so the pattern is: code for a word = sum of letter positions + 2. Step 7: Compute the sum for BOAT. B = 2, O = 15, A = 1, T = 20, total = 2 + 15 + 1 + 20 = 38. Step 8: Add 2 to this sum: 38 + 2 = 40. So BOAT is coded as 40.

Verification / Alternative check:
We have already verified the rule on both given examples, which is essential. In many exam questions, if one simple arithmetic rule fits all the given data, it is almost certainly the intended pattern. There is no need to search for a more complicated relationship when a neat and consistent rule already works. If we tried alternate possibilities such as sum of consonants or product of digits, they would not match both 45 and 41 simultaneously, so the sum plus two pattern is clearly the most reasonable and consistent interpretation.

Why Other Options Are Wrong:
Option 41 would be correct only if the sum for BOAT were 39, but we calculated 38. Option 42, 43 and 44 would require adding 4, 5 or 6 instead of 2, and that would break the pattern observed in GOAT and COAT. The entire point is that the same constant is added in each case. Thus options 41, 42, 43 and 44 do not obey the rule that is consistent across all examples, and only 40 matches the required pattern.

Common Pitfalls:
A common mistake is to look only at GOAT and build a pattern that works for it alone without checking COAT. Another frequent error is to guess that the code might depend on the number of vowels or consonants, which can be tempting but is not supported by the numerical values here. Candidates sometimes forget the constant adjustment and try to make the sum of letter positions equal the code directly, which fails in these examples. Always verify a proposed rule against every piece of given data before trusting it.

Final Answer:
Using the rule code = sum of alphabetical positions + 2, the word BOAT is written as 40 in the given code language.