Understanding the Coding Decoding Problem

This question is a type of coding-decoding problem, specifically a letter-to-number coding. We are given two words, FROG and RANG, and their corresponding numerical codes. Our task is to identify the pattern or rule governing this coding and then apply it to find the code for the word FORT.

The given information is:

• FROG is coded as 9268
• RANG is coded as 2538
• We need to find the code for FORT.

Analyzing the Given Codes to Find the Pattern

Let's compare the letters in the words with the digits in their respective codes:

For FROG (9268):

• F → ?
• R → ?
• O → ?
• G → ?

For RANG (2538):

• R → ?
• A → ?
• N → ?
• G → ?

We look for letters common to both words and see if they correspond to the same digit in their codes. The letters 'R' and 'G' are present in both FROG and RANG.

• In FROG (9268), R is the second letter and its code is 2. G is the fourth letter and its code is 8.
• In RANG (2538), R is the first letter and its code is 2. G is the fourth letter and its code is 8.

Since 'R' is consistently coded as 2 and 'G' is consistently coded as 8 in both words, it suggests a direct letter-to-digit substitution where each letter has a unique corresponding digit.

Deriving the Letter-to-Digit Mapping

Based on the consistent coding of R and G, we can deduce the codes for the other letters from the given information:

From FROG ∶ 9268:

• F → 9 (First letter of FROG is F, first digit is 9)
• R → 2 (Second letter of FROG is R, second digit is 2 - confirmed)
• O → 6 (Third letter of FROG is O, third digit is 6)
• G → 8 (Fourth letter of FROG is G, fourth digit is 8 - confirmed)

From RANG ∶ 2538:

• R → 2 (First letter of RANG is R, first digit is 2 - confirmed)
• A → 5 (Second letter of RANG is A, second digit is 5)
• N → 3 (Third letter of RANG is N, third digit is 3)
• G → 8 (Fourth letter of RANG is G, fourth digit is 8 - confirmed)

So, the derived letter-to-digit mappings are:

Coding the Word FORT

Now, we need to find the code for the word FORT using the mappings we derived. The word FORT consists of the letters F, O, R, and T.

• For F, the code is 9.
• For O, the code is 6.
• For R, the code is 2.
• For T, the letter 'T' is not present in the source words FROG or RANG. We need to look at the options provided to see if the code for T can be inferred. The options are 9327, 9762, 9672, and 9627.

Let's apply the codes for F, O, and R to the word FORT:

• F → 9
• O → 6
• R → 2

So, the code for FORT should start with 962. Let's look at the options:

• Option 1: 9327 (Starts with 932) - Doesn't match 962.
• Option 2: 9762 (Starts with 976) - Doesn't match 962.
• Option 3: 9672 (Starts with 967) - Doesn't match 962.
• Option 4: 9627 (Starts with 962) - Matches 962. The last digit is 7.

This suggests that the code for T is 7. Let's confirm the complete mapping based on Option 4:

• F → 9
• O → 6
• R → 2
• T → 7

Putting these together for FORT:

F $\rightarrow$ 9

O $\rightarrow$ 6

R $\rightarrow$ 2

T $\rightarrow$ 7

The code for FORT is 9627.

Conclusion: The Code for FORT

By analyzing the given codes for FROG and RANG, we determined the letter-to-digit mapping for F, R, O, G, A, and N. By applying this mapping to the word FORT and examining the options, we inferred the code for the letter T. The resulting code for FORT is 9627, which matches one of the provided options.

Revision Table: Letter Codes

Additional Information: Types of Coding Decoding

Coding-decoding questions are common in reasoning sections of competitive exams. They test your ability to identify patterns and rules in how information is coded. Some common types include:

• Letter Coding: Letters are coded using other letters based on patterns (e.g., shifting positions in the alphabet, reversing order).
• Number Coding: Words or letters are coded using numbers (as seen in this question). The pattern might be direct letter-to-digit substitution, positional value, or arithmetic operations.
• Symbol Coding: Letters or words are coded using symbols.
• Mixed Coding: Words are coded using a mix of letters, numbers, and symbols.

Solving these problems often involves comparing the given words and codes, finding common elements, and testing potential rules like substitution, rearrangement, or arithmetic operations.