Understanding the Coding System

This question involves a simple substitution coding system where each word is represented by a unique digit. To find the code for a specific word, we need to compare the given phrases and their corresponding codes to identify the common words and their associated digits.

Analyzing the Given Information

We are given three coded phrases:

• 'how are you' is coded as '639'.
• 'are you fine today' is coded as '6453'.
• 'stay fine' is coded as '58'.

Step-by-Step Decoding Process

Let's compare the phrases and their codes:

Step 1: Compare the first and second phrases.

• Phrase 1: 'how are you' (639)
• Phrase 2: 'are you fine today' (6453)

The common words in Phrase 1 and Phrase 2 are 'are' and 'you'. The common digits in their codes (639 and 6453) are 6 and 3. This means 'are' and 'you' are coded as 6 and 3, but we don't know which word gets which digit yet.

Step 2: Compare the second and third phrases.

• Phrase 2: 'are you fine today' (6453)
• Phrase 3: 'stay fine' (58)

The common word in Phrase 2 and Phrase 3 is 'fine'. The common digit in their codes (6453 and 58) is 5. Therefore, the code for 'fine' is 5.

Step 3: Deduce the code for 'stay'.

• Phrase 3: 'stay fine' (58)

We know that 'fine' is coded as 5. In the code '58', if 5 represents 'fine', then the remaining digit 8 must represent 'stay'. So, the code for 'stay' is 8.

Step 4: Deduce the code for 'today'.

• Phrase 2: 'are you fine today' (6453)

From previous steps, we know:

• 'are' and 'you' are coded as 6 and 3 (in some order).
• 'fine' is coded as 5.

In the code '6453', the digits 6, 3, and 5 correspond to 'are', 'you', and 'fine'. The only remaining digit in the code is 4, and the only remaining word in the phrase is 'today'. Therefore, the code for 'today' is 4.

Step 5: Deduce the code for 'how'. (Optional, but confirms the system)

• Phrase 1: 'how are you' (639)

We know that 'are' and 'you' are coded as 6 and 3. In the code '639', if 6 and 3 represent 'are' and 'you', the remaining digit 9 must represent 'how'. So, the code for 'how' is 9.

Summary of Codes

Based on our analysis, the codes for the words are:

• how: 9
• are/you: 6 or 3
• fine: 5
• today: 4
• stay: 8

Conclusion

We were asked for the code for 'Today'. Based on our decoding process, the code for 'Today' is 4.

Revision Table: Coding Decoding

Reviewing the key steps and results:

Additional Information on Coding Systems

Coding and decoding questions often appear in reasoning sections of competitive exams. These questions test your ability to identify patterns and apply logical deduction. Common types include:

• Letter Coding: Letters are replaced by other letters based on a pattern (e.g., shifting positions in the alphabet).
• Number Coding: Words are coded using numbers based on letter positions, values, or other rules.
• Symbol Coding: Letters or words are replaced by symbols.
• Substitution Coding: As seen in this problem, where specific words/letters are directly substituted with others (numbers, letters, or symbols).

Solving such problems requires careful observation, comparison of given examples, and systematic elimination to find the rule or mapping.