Understanding the Coding Logic for TURKEY and BREATH

This question involves a coding-decoding pattern where letters are represented by numbers. We are given the word 'TURKEY' is coded as '76911525' and need to find the code for 'BREATH' using the same logic.

Let's analyze the letters in 'TURKEY' and compare them with the numerical code '76911525'. The word 'TURKEY' has 6 letters, while the code has 8 digits. This suggests that some letters might be represented by single digits and others by double digits.

Analyzing the Code for TURKEY

Let's look at the alphabetical position of each letter in 'TURKEY':

• T is the 20th letter.
• U is the 21st letter.
• R is the 18th letter.
• K is the 11th letter.
• E is the 5th letter.
• Y is the 25th letter.

The alphabetical positions are 20, 21, 18, 11, 5, 25. The code is 76911525.

Let's try to see if there's a pattern using original or reverse alphabetical positions. The reverse alphabetical position of a letter is calculated as $\text{27} - \text{its original position}$.

• Reverse position of T: $\text{27} - \text{20} = \text{7}$
• Reverse position of U: $\text{27} - \text{21} = \text{6}$
• Reverse position of R: $\text{27} - \text{18} = \text{9}$
• Reverse position of K: $\text{27} - \text{11} = \text{16}$
• Reverse position of E: $\text{27} - \text{5} = \text{22}$
• Reverse position of Y: $\text{27} - \text{25} = \text{2}$

Comparing the original positions (20, 21, 18, 11, 5, 25) and reverse positions (7, 6, 9, 16, 22, 2) with the code '76911525', we can observe a pattern:

• The code starts with '769'. This matches the reverse positions of T (7), U (6), and R (9).
• The next part of the code is '11'. This matches the original position of K (11).
• The next part is '5'. This matches the original position of E (5).
• The last part is '25'. This matches the original position of Y (25).

So, the coding logic appears to be:

• The first three letters are coded using their reverse alphabetical positions.
• The remaining letters are coded using their original alphabetical positions.

Let's verify this logic with 'TURKEY':

Concatenating the code digits gives 76911525, which matches the given code for 'TURKEY'. The logic is confirmed.

Applying the Logic to BREATH

Now, let's apply the same logic to the word 'BREATH'. 'BREATH' also has 6 letters.

We need the alphabetical positions of the letters in 'BREATH':

• B is the 2nd letter.
• R is the 18th letter.
• E is the 5th letter.
• A is the 1st letter.
• T is the 20th letter.
• H is the 8th letter.

Apply the logic: First three letters use reverse position, remaining letters use original position.

• B (1st letter): Reverse position = $\text{27} - \text{2} = \text{25}$
• R (2nd letter): Reverse position = $\text{27} - \text{18} = \text{9}$
• E (3rd letter): Reverse position = $\text{27} - \text{5} = \text{22}$
• A (4th letter): Original position = $\text{1}$
• T (5th letter): Original position = $\text{20}$
• H (6th letter): Original position = $\text{8}$

The code digits are 25, 9, 22, 1, 20, 8.

Concatenate these digits to get the code for 'BREATH': 259221208.

Comparing with Options

Let's check the given options:

1. 259221208
2. 259221197
3. 218526208
4. 251841208

Our calculated code, 259221208, matches the first option.

Conclusion on BREATH Coding

Following the identified coding pattern from 'TURKEY' to '76911525', the word 'BREATH' is coded by taking the reverse alphabetical positions for the first three letters (B, R, E) and the original alphabetical positions for the remaining letters (A, T, H). This results in the code 259221208.

Revision Table: Coding-Decoding Pattern

Additional Information on Coding-Decoding Reasoning

Coding-decoding questions are common in reasoning sections of competitive exams. They test your ability to identify patterns in how words, letters, or numbers are translated into a code. Common types of coding include:

• Letter Coding: Letters are replaced by other letters based on a pattern (e.g., shifting positions in the alphabet).
• Number Coding: Words or letters are coded using numbers, often based on their alphabetical positions (original or reverse), sum of positions, or other arithmetic operations.
• Mixed Coding: A combination of letter and number coding, or different rules applied within the same word as seen in this problem.
• Substitution Coding: Words are directly substituted with other words.

To solve coding-decoding problems, it is essential to:

• Know the alphabetical order and position of each letter (A=1, B=2, ..., Z=26).
• Be familiar with reverse alphabetical positions (A=26, B=25, ..., Z=1).
• Look for patterns such as shifting, reverse order, sum of positions, difference in positions, or specific rules applied to vowels/consonants or positions within the word.
• Compare the given word and its code carefully to deduce the underlying rule.
• Apply the same rule consistently to the word you need to code.