Understanding the Code Language Pattern

The question describes a specific code language where words are converted into numerical codes. We are given two examples: 'ALPINE' is coded as '171' and 'SPRING' is coded as '83'. Our task is to find the code for 'CAPITAL' using the same logic.

Analyzing the Given Codes: ALPINE and SPRING

Let's analyze how 'ALPINE' and 'SPRING' are coded to find the underlying pattern. A common approach in such coding-decoding problems is to use the alphabetical positions of the letters (A=1, B=2, ..., Z=26).

Code for ALPINE (171)

First, let's find the alphabetical positions of the letters in 'ALPINE':

• A = 1
• L = 12
• P = 16
• I = 9
• N = 14
• E = 5

Now, let's sum these positions:

\( \text{Sum for ALPINE} = 1 + 12 + 16 + 9 + 14 + 5 = 57 \)

The coded value is 171. Notice that \( 171 = 57 \times 3 \). Let's look for a reason for this multiplier, '3'.

Let's count the number of vowels (A, E, I, O, U) in 'ALPINE'. The vowels are A, I, E. There are 3 vowels.

It appears the code for 'ALPINE' might be the sum of the alphabetical positions multiplied by the number of vowels.

\( \text{Code for ALPINE} = (\text{Sum of positions}) \times (\text{Number of vowels}) = 57 \times 3 = 171 \)

This matches the given code for ALPINE.

Code for SPRING (83)

Let's test this pattern with 'SPRING'. Find the alphabetical positions:

• S = 19
• P = 16
• R = 18
• I = 9
• N = 14
• G = 7

Sum the positions:

\( \text{Sum for SPRING} = 19 + 16 + 18 + 9 + 14 + 7 = 83 \)

The coded value for SPRING is 83. Let's count the number of vowels in 'SPRING'. The only vowel is I. There is 1 vowel.

Using the proposed pattern:

\( \text{Code for SPRING} = (\text{Sum of positions}) \times (\text{Number of vowels}) = 83 \times 1 = 83 \)

This also matches the given code for SPRING.

The pattern is consistent: The code for a word is the sum of the alphabetical positions of its letters multiplied by the number of vowels in the word.

Coding CAPITAL using the Discovered Pattern

Now, let's apply this pattern to find the code for 'CAPITAL'.

First, find the alphabetical positions of the letters in 'CAPITAL':

• C = 3
• A = 1
• P = 16
• I = 9
• T = 20
• A = 1
• L = 12

Next, calculate the sum of these positions:

\( \text{Sum for CAPITAL} = 3 + 1 + 16 + 9 + 20 + 1 + 12 = 62 \)

Now, count the number of vowels in 'CAPITAL'. The vowels are A, I, A. There are 3 vowels.

Finally, apply the pattern (Sum of positions \(\times\) Number of vowels) to find the code for 'CAPITAL':

\( \text{Code for CAPITAL} = 62 \times 3 \)

\( \text{Code for CAPITAL} = 186 \)

The code for 'CAPITAL' is 186.

Comparing with Options

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

• Option 1: 93
• Option 2: 124
• Option 3: 186
• Option 4: 62

Our calculated code, 186, matches Option 3.

Detailed Steps for Coding Words

Here's a summary of the steps involved in coding a word in this language:

1. Identify each letter in the word.
2. Find the standard alphabetical position (A=1, B=2, ...) for each letter.
3. Calculate the sum of these alphabetical positions.
4. Count the number of vowels (A, E, I, O, U) in the word.
5. Multiply the sum of positions (Step 3) by the number of vowels (Step 4). The result is the code.

Revision Table: Coding Examples

Additional Information on Coding Patterns

Coding-decoding questions in competitive exams often use various patterns based on alphabetical positions, letter types (vowels/consonants), or other letter properties. Some common patterns include:

• Sum of alphabetical positions (forward or reverse).
• Sum of positions multiplied or divided by a fixed number.
• Sum of positions multiplied or divided by the number of letters.
• Sum of positions multiplied or divided by the number of vowels or consonants.
• Patterns involving reverse alphabetical positions (A=26, B=25, ...).
• Adding or subtracting a fixed number from each letter's position.
• Patterns involving the number of consonants.
• Interchanging letters or blocks of letters.

Careful observation and testing different simple patterns using the given examples are key to solving these types of questions.