Understanding Coding-Decoding Patterns

This question involves a type of coding-decoding where words are assigned numerical values based on a specific pattern or rule. To solve this, we need to analyze the given examples to identify the underlying logic.

Analyzing the Given Codes

We are given two examples:

• 'WASTE' is coded as '60'.
• 'BRANDED' is coded as '84'.

Our goal is to find the code for 'CEILINGFANS'.

Checking Common Coding Patterns

Let's explore potential patterns, such as summing up positional values of letters (A=1, B=2, ..., Z=26) or reverse positional values (A=26, B=25, ..., Z=1).

Let's look at the word 'WASTE':

• Letters are W, A, S, T, E.
• Number of letters = 5.
• Positional values: W=23, A=1, S=19, T=20, E=5.
• Sum of positional values = $23 + 1 + 19 + 20 + 5 = 68$.
• Reverse positional values: W=4, A=26, S=8, T=7, E=22.
• Sum of reverse positional values = $4 + 26 + 8 + 7 + 22 = 67$.

Neither the sum of positional values (68) nor the sum of reverse positional values (67) matches the given code (60).

Now, let's look at the word 'BRANDED':

• Letters are B, R, A, N, D, E, D.
• Number of letters = 7.
• Positional values: B=2, R=18, A=1, N=14, D=4, E=5, D=4.
• Sum of positional values = $2 + 18 + 1 + 14 + 4 + 5 + 4 = 48$.
• Reverse positional values: B=25, R=9, A=26, N=13, D=23, E=22, D=23.
• Sum of reverse positional values = $25 + 9 + 26 + 13 + 23 + 22 + 23 = 141$.

Again, neither sum matches the code (84).

Discovering the Coding Rule

Let's look at the given codes (60 and 84) in relation to the number of letters in each word:

• For 'WASTE': Code = 60, Number of letters = 5. Notice that $60 \div 5 = 12$.
• For 'BRANDED': Code = 84, Number of letters = 7. Notice that $84 \div 7 = 12$.

It appears the code for a word is obtained by multiplying the number of letters in the word by 12.

The rule is: Code = Number of letters $\times$ 12.

Applying the Rule to CEILINGFANS

Now let's apply this rule to the word 'CEILINGFANS'.

• Count the number of letters in 'CEILINGFANS': C, E, I, L, I, N, G, F, A, N, S.
• There are 11 letters in 'CEILINGFANS'.

Using the discovered rule:

Code for 'CEILINGFANS' = Number of letters $\times$ 12

Code for 'CEILINGFANS' = $11 \times 12$

Code for 'CEILINGFANS' = $132$

Therefore, the code for 'CEILINGFANS' is 132.

Conclusion

Based on the pattern observed in the examples, the code for 'CEILINGFANS' is 132.

Revision Table: Key Concepts in Coding-Decoding

Additional Information: Types of Coding-Decoding Questions

Coding-decoding questions test your ability to decipher a rule or pattern hidden in a set of coded messages. Common types include:

• Letter Coding: Letters are replaced by other letters.
• Number/Symbol Coding: Words or letters are replaced by numbers or symbols. This problem is an example of Word-to-Number coding.
• Mixed Coding: Words and codes are given in sentences, and you need to find the code for specific words.
• Substitution Coding: One word is substituted for another (e.g., 'red' is called 'blue').

Practicing different types helps in quickly identifying the pattern during exams.