Solving Coding-Decoding Puzzles

This question is a classic example of a coding-decoding puzzle where letters are assigned numerical values based on a hidden pattern. We are given the codes for 'BRAVE' and 'BOTH' and need to find the code for 'ABACUS' using the same rule.

Analyzing the Given Codes: BRAVE and BOTH

Let's look at the words and their assigned numerical codes:

• BRAVE is coded as 43.
• BOTH is coded as 41.

We need to find the pattern that relates the letters of the words to these numbers.

Testing Common Coding Patterns

Often, coding patterns involve the alphabetical position of letters. Let's consider the standard alphabetical position (A=1, B=2, ..., Z=26).

Sum of standard positions for BRAVE:

\( \text{Sum} = 2 + 18 + 1 + 22 + 5 = 48 \)

The code for BRAVE is 43, which is \( 48 - 5 \). Notice that 5 is the number of letters in the word 'BRAVE'.

Let's test this pattern with the second word, BOTH.

Sum of standard positions for BOTH:

\( \text{Sum} = 2 + 15 + 20 + 8 = 45 \)

The code for BOTH is 41, which is \( 45 - 4 \). Notice that 4 is the number of letters in the word 'BOTH'.

The pattern seems consistent: The code is the sum of the standard alphabetical positions of the letters minus the total number of letters in the word.

\( \text{Code} = (\text{Sum of Standard Positions}) - (\text{Number of Letters}) \)

Applying the Code Pattern to ABACUS

Now, let's apply this rule to find the code for 'ABACUS'.

First, find the standard alphabetical position for each letter in ABACUS:

Calculate the sum of these positions:

\( \text{Sum} = 1 + 2 + 1 + 3 + 21 + 19 = 47 \)

Next, count the number of letters in 'ABACUS'. There are 6 letters.

Finally, apply the derived coding rule:

\( \text{Code for ABACUS} = (\text{Sum of Standard Positions}) - (\text{Number of Letters}) \)

\( \text{Code for ABACUS} = 47 - 6 = 41 \)

Thus, the code for 'ABACUS' is 41.

Checking the Options

Let's compare our result with the given options:

• Option 1: 43
• Option 2: 47
• Option 3: 41
• Option 4: 31

Our calculated code, 41, matches Option 3.

Final Answer

Based on the pattern observed in the coding of 'BRAVE' and 'BOTH', the word 'ABACUS' is coded as 41.

Revision Table: Coding-Decoding Logic

Additional Information: Types of Coding-Decoding

Coding-decoding is a common topic in logical reasoning for competitive exams. Understanding different types of coding helps in quickly identifying the pattern. Some common types include:

• Letter Coding: Letters are coded based on their position, shift, or other rules. (Like the current problem involving alphabetical position).
• Number Coding: Words or letters are coded using numbers. This can involve sum/difference of positions, number of vowels/consonants, etc.
• Symbol Coding: Letters or words are represented using symbols.
• Substitution Coding: One word is substituted for another (e.g., 'sky' is called 'blue').
• Mixed Letter and Number Coding: A combination of letter and number rules.

Practice with various types of questions is key to mastering coding-decoding skills.