Decoding Letter Patterns: GANGA, KOSHI, and GOMTI

This problem involves understanding a specific code language where words are represented by sequences of numbers. We are given two examples to figure out the rule and then apply it to a new word, 'GOMTI'.

Analyzing the Given Codes

Let's look at the first example:

• The word is 'GANGA'.
• The code is 21-3-42-21-3.

And the second example:

• The word is 'KOSHI'.
• The code is 33-45-57-24-27.

We need to find the relationship between the letters of the words and the numbers in their codes.

Finding the Coding Rule

A common approach in such coding problems is to consider the alphabetical position of each letter. Let's list the standard alphabetical positions for the letters in 'GANGA' and 'KOSHI':

Comparing the standard positions of 'GANGA' (7, 1, 14, 7, 1) with its code (21, 3, 42, 21, 3), we can see a pattern:

• For G (position 7), the code is 21. ($7 \times 3 = 21$)
• For A (position 1), the code is 3. ($1 \times 3 = 3$)
• For N (position 14), the code is 42. ($14 \times 3 = 42$)
• For G (position 7), the code is 21. ($7 \times 3 = 21$)
• For A (position 1), the code is 3. ($1 \times 3 = 3$)

It appears the rule is to multiply the standard alphabetical position of each letter by 3.

Let's verify this rule with the second word, 'KOSHI'. Its standard alphabetical positions are K=11, O=15, S=19, H=8, I=9.

The calculated codes for 'KOSHI' (33, 45, 57, 24, 27) perfectly match the given code. So, the rule is confirmed: each letter is coded by multiplying its standard alphabetical position by 3.

Coding the Word 'GOMTI'

Now we apply the same rule to the word 'GOMTI'. First, find the standard alphabetical position for each letter:

• G: 7
• O: 15
• M: 13
• T: 20
• I: 9

Next, multiply each position by 3 to get the code:

• G: $7 \times 3 = 21$
• O: $15 \times 3 = 45$
• M: $13 \times 3 = 39$
• T: $20 \times 3 = 60$
• I: $9 \times 3 = 27$

Putting the codes together, 'GOMTI' is coded as 21-45-39-60-27.

Final Answer Derivation

Based on our analysis and application of the coding rule, the code for 'GOMTI' is 21-45-39-60-27. We check the given options to find the matching code.

Revision Table: Coding Rule Summary

Additional Information: Letter Coding Techniques

Coding and decoding problems often involve relationships between letters and numbers. Some common techniques include:

• Alphabetical Position: Using the standard position (A=1, B=2, etc.) or reverse position (A=26, B=25, etc.).
• Operations on Positions: Adding, subtracting, multiplying, or dividing the positions by a constant number.
• Sum of Positions: Coding a word by summing the positions of its letters.
• Pattern-Based Replacement: Replacing letters with other letters based on a shift (like Caesar cipher) or a more complex pattern.
• Consonant/Vowel Rules: Different rules for consonants and vowels.

Solving these problems requires careful observation of the examples to identify the specific rule or pattern being used.