Decoding the Pattern in Letter Coding

This problem involves a type of coding where words are represented by numbers. We are given the codes for 'ROSE' and 'TULIP' and need to find the code for 'LOTUS'. We need to identify the underlying pattern or logic used for encoding.

Analyzing the Given Codes: ROSE and TULIP

Let's first consider the positional values of the letters in the English alphabet (A=1, B=2, ..., Z=26).

• ROSE:
  • R is the 18th letter.
  • O is the 15th letter.
  • S is the 19th letter.
  • E is the 5th letter.
  Sum of letter values for ROSE: $\text{Sum} = 18 + 15 + 19 + 5 = 57$. The given code for ROSE is 228. Let's see how 57 relates to 228. $\frac{228}{57} = 4$. The number of letters in ROSE is 4. It seems the coded value is the sum of letter values multiplied by the number of letters in the word.
• TULIP:
  • T is the 20th letter.
  • U is the 21st letter.
  • L is the 12th letter.
  • I is the 9th letter.
  • P is the 16th letter.
  Sum of letter values for TULIP: $\text{Sum} = 20 + 21 + 12 + 9 + 16 = 78$. The given code for TULIP is 390. Let's see how 78 relates to 390. $\frac{390}{78} = 5$. The number of letters in TULIP is 5. This observation matches the pattern found with ROSE. The coded value seems to be the sum of letter values multiplied by the number of letters.

Identifying the Coding Rule

Based on the analysis of 'ROSE' and 'TULIP', the coding rule appears to be:

Coded Value = (Sum of positional values of letters) × (Number of letters in the word)

Applying the Code to LOTUS

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

• LOTUS:
  • L is the 12th letter.
  • O is the 15th letter.
  • T is the 20th letter.
  • U is the 21st letter.
  • S is the 19th letter.
  Sum of letter values for LOTUS: $\text{Sum} = 12 + 15 + 20 + 21 + 19 = 87$. The number of letters in LOTUS is 5.

Using the coding rule:

Coded Value for LOTUS = (Sum of letter values) × (Number of letters)

Coded Value for LOTUS = $87 \times 5$

Coded Value for LOTUS = $435$

Therefore, 'LOTUS' will be coded as 435.

Summary of Calculation Steps

Final Answer Derivation

Based on our calculation, the code for 'LOTUS' is 435.

Revision Table: Key Coding Concepts

Additional Information: Types of Coding-Decoding

Coding-decoding questions test your ability to decipher rules and patterns in how letters, words, or numbers are transformed. Common types include:

• Letter Coding: Letters are replaced by other letters based on a specific rule (e.g., shifting positions, opposite letters).
• Number Coding: Words are coded using numbers based on rules like letter positions, sum of positions, number of vowels/consonants, etc. (as seen in this problem).
• Symbol Coding: Letters or words are coded using symbols.
• Substitution Coding: Words are substituted with other words (e.g., 'red' is called 'blue').
• Mixed Coding: Sentences are coded, and you need to find the code for individual words by comparing different sentences.

Solving these problems requires careful observation, analysis, and systematic testing of possible patterns.