Understanding Coding and Decoding Logic

This question asks us to decode a word based on a given example of coding. We are given that in a certain code language, the word 'PEN' is coded as '321028'. We need to find the code for the word 'TUB' using the same logic.

To solve this type of coding decoding problem, we first need to analyze the relationship between the original word 'PEN' and its code '321028'. This could involve the alphabetical positions of the letters, mathematical operations, or other patterns.

Analyzing the Coding Pattern for 'PEN'

Let's look at the letters in 'PEN' and their positions in the English alphabet:

• P is the 16th letter.
• E is the 5th letter.
• N is the 14th letter.

The given code for 'PEN' is '321028'. Let's try to see if there is a mathematical relationship between the alphabetical positions (16, 5, 14) and the parts of the code (which appears to be split into groups of digits).

The code '321028' can potentially be broken down into segments corresponding to each letter:

• For 'P' (16th letter), the code part seems to be '32'. Notice that $16 \times 2 = 32$.
• For 'E' (5th letter), the code part seems to be '10'. Notice that $5 \times 2 = 10$.
• For 'N' (14th letter), the code part seems to be '28'. Notice that $14 \times 2 = 28$.

It appears the logic is to find the alphabetical position of each letter, multiply it by 2, and then concatenate the resulting numbers to form the code word. Let's verify this logic with 'PEN'.

P → Position 16 → $16 \times 2 = 32$
E → Position 5 → $5 \times 2 = 10$
N → Position 14 → $14 \times 2 = 28$

Concatenating these results (32, 10, 28) gives '321028', which matches the given code for 'PEN'. So, this appears to be the correct coding logic.

Applying the Coding Logic to 'TUB'

Now, let's apply this same logic to find the code for the word 'TUB'. First, find the alphabetical position of each letter in 'TUB':

• T is the 20th letter.
• U is the 21st letter.
• B is the 2nd letter.

Next, multiply each position number by 2:

• T → Position 20 → $20 \times 2 = 40$
• U → Position 21 → $21 \times 2 = 42$
• B → Position 2 → $2 \times 2 = 4$

Finally, concatenate the resulting numbers (40, 42, 4) in order:

40 followed by 42 followed by 4 results in the code '40424'.

Comparing with Options

Let's compare our calculated code '40424' with the given options:

• Option 1: 40424
• Option 2: 42404
• Option 3: 40422
• Option 4: 44024

Our calculated code '40424' matches Option 1.

Step-by-Step Solution Summary

1. Identify the original word ('PEN') and its code ('321028').
2. Determine the alphabetical position of each letter in 'PEN' (P=16, E=5, N=14).
3. Analyze the relationship between positions and the code. The pattern found is Position $\times$ 2.
4. Verify the pattern: $16 \times 2 = 32$, $5 \times 2 = 10$, $14 \times 2 = 28$. Concatenating these (321028) matches the given code.
5. Apply the same logic to the word 'TUB'.
6. Find the alphabetical position of each letter in 'TUB' (T=20, U=21, B=2).
7. Multiply each position by 2: $20 \times 2 = 40$, $21 \times 2 = 42$, $2 \times 2 = 4$.
8. Concatenate the results (40, 42, 4) to get the code '40424'.
9. Match the calculated code with the given options.

The code for 'TUB' is 40424.

Revision Table: Coding Decoding Basics

Additional Information: Types of Coding Decoding

Coding and decoding questions are common in competitive exams and test logical reasoning. There are several types of coding patterns you might encounter:

• Letter Coding: Letters are coded using other letters. This can involve shifting positions (e.g., A → C), reversing alphabetical order, or other patterns.
• Number/Symbol Coding: Words or letters are coded using numbers or symbols, as seen in this problem. The code might be based on alphabetical position, numerical value of letters, or assigned values.
• Mixed Coding: Words are coded using a mix of letters and numbers/symbols.
• Substitution Coding: One word is substituted for another (e.g., 'Red is called Blue', 'Blue is called Green').
• Sentence Coding: A full sentence or phrase is coded, usually by assigning codes to individual words within the sentence.

Solving these problems requires careful observation, pattern recognition, and systematic application of the discovered rule.