Decoding the Code Language: 'FUEL', 'JEER', and 'FARE'

This question involves a coding language where words are assigned numerical values based on a specific rule. We are given the codes for 'FUEL' and 'JEER' and need to find the code for 'FARE' using the same rule.

Analyzing the Given Codes

Let's first determine the numerical values of the letters based on their position in the English alphabet (A=1, B=2, ..., Z=26).

• F = 6
• U = 21
• E = 5
• L = 12
• J = 10
• R = 18
• A = 1

Applying Letter Values to 'FUEL'

Let's sum the alphabetical positions for the letters in 'FUEL':

Sum for 'FUEL' = Value of F + Value of U + Value of E + Value of L

Sum for 'FUEL' = \(6 + 21 + 5 + 12 = 44\)

The given code for 'FUEL' is 50. The difference between the code and the sum of positions is \(50 - 44 = 6\).

Applying Letter Values to 'JEER'

Now let's do the same for 'JEER':

Sum for 'JEER' = Value of J + Value of E + Value of E + Value of R

Sum for 'JEER' = \(10 + 5 + 5 + 18 = 38\)

The given code for 'JEER' is 44. The difference between the code and the sum of positions is \(44 - 38 = 6\).

Identifying the Coding Rule

Based on the analysis of 'FUEL' and 'JEER', it appears that the coding rule is:

Code = (Sum of alphabetical positions of letters in the word) + 6

Calculating the Code for 'FARE'

Now, we apply this rule to the word 'FARE'. First, let's find the sum of the alphabetical positions for the letters in 'FARE':

Sum for 'FARE' = Value of F + Value of A + Value of R + Value of E

Sum for 'FARE' = \(6 + 1 + 18 + 5 = 30\)

Using the identified coding rule:

Code for 'FARE' = Sum for 'FARE' + 6

Code for 'FARE' = \(30 + 6 = 36\)

Therefore, the word 'FARE' is coded as '36' in this language.

Revision Table: Coding Language Rules

The consistent difference of 6 confirms the rule: Code = Sum of letter positions + 6.

Additional Information: Types of Coding Questions

Coding and decoding questions in reasoning often test your ability to find patterns and rules. Common types include:

• Letter Coding: Replacing letters with other letters based on a shift or pattern.
• Number Coding: Assigning numerical values to letters or words based on their position, sum of positions, or other calculations.
• Symbol Coding: Using symbols instead of letters or numbers.
• Mixed Coding: Combining letters, numbers, and symbols.

To solve these questions, always start by comparing the original word/number/symbol with its coded form and look for consistent patterns or mathematical operations.