Understanding the Coding-Decoding Pattern

This question is an example of coding-decoding, where words are assigned numerical values based on a specific pattern or rule. We are given the codes for 'LOST' and 'CRAMP' and need to find the code for 'FRY' using the same rule.

Analyzing the Given Codes

We are given the following information:

• 'LOST' is coded as ‘32’
• 'CRAMP' is coded as ‘50’

We need to find the code for 'FRY'.

Searching for the Pattern

Let's first look at the letters and their positions in the English alphabet (A=1, B=2, ..., Z=26).

• LOST: L=12, O=15, S=19, T=20. The sum of these positions is $12 + 15 + 19 + 20 = 66$. The given code is 32.
• CRAMP: C=3, R=18, A=1, M=13, P=16. The sum of these positions is $3 + 18 + 1 + 13 + 16 = 51$. The given code is 50.

The codes (32 and 50) are not directly the sum of the letter positions (66 and 51).

Let's consider the number of letters in each word:

• 'LOST' has 4 letters. Code = 32.
• 'CRAMP' has 5 letters. Code = 50.

Let's see if there is a relationship between the number of letters and the code:

• For 'LOST' (4 letters), $\frac{32}{4} = 8$.
• For 'CRAMP' (5 letters), $\frac{50}{5} = 10$.

The result of dividing the code by the number of letters gives 8 and 10. Notice that the number 10 is 2 more than 8. This suggests a pattern where the multiplier is related to the number of letters.

Let N be the number of letters in the word. The pattern appears to be:

Code = N $\times$ Multiplier

Where the Multiplier increases by 2 as N increases by 1 (from 4 to 5).

• For N=4, Multiplier = 8. So, Code = $4 \times 8 = 32$.
• For N=5, Multiplier = 10. So, Code = $5 \times 10 = 50$.

We can observe that the Multiplier for N letters seems to be $2 \times N$. Let's verify this rule:

• For 'LOST' (N=4), Multiplier = $2 \times 4 = 8$. Code = $4 \times 8 = 32$. This matches the given code.
• For 'CRAMP' (N=5), Multiplier = $2 \times 5 = 10$. Code = $5 \times 10 = 50$. This also matches the given code.

So the pattern is: Code = Number of letters $\times$ (2 $\times$ Number of letters), which simplifies to Code = (Number of letters)$^2 \times 2$.

Applying the Pattern to 'FRY'

Now, let's apply this pattern to the word 'FRY'.

The word 'FRY' has 3 letters. So, N = 3.

Using the pattern: Code = (Number of letters)$^2 \times 2$

Code for 'FRY' = $3^2 \times 2 = 9 \times 2 = 18$.

Conclusion

Based on the pattern observed from 'LOST' and 'CRAMP', the code for 'FRY' is 18.

The correct option is 18.

Revision Table: Coding-Decoding Concepts

Additional Information: Types of Coding

Coding-decoding questions test your ability to identify patterns. Some common types include:

• Letter Coding: Letters are replaced by other letters based on a shift in position (e.g., A becomes B, C becomes D, etc.) or a mixed-up alphabet.
• Number Coding: Words are assigned numerical values. This can be based on letter positions, sum of positions, number of letters, sum/product of digits of positions, or other arithmetic operations.
• Symbol Coding: Letters or words are coded using symbols.
• Mixed Coding: Words, numbers, and symbols are used in combination to form codes.

Solving these questions requires careful observation, logical reasoning, and testing different possible patterns using the given examples.