This is a coding and decoding question where words are assigned numerical values based on a specific pattern or rule. We are given two examples of how words are coded, and we need to use these examples to figure out the coding rule. Once the rule is identified, we can apply it to find the code for the word "REVERSE".

Analyzing the Coding Pattern

Let's look at the given examples:

• TOGETHER is coded as 119
• MASTER is coded as 87

We need to find a connection between the letters of the word and the assigned number. Common patterns involve the alphabetical position of letters (A=1, B=2, ..., Z=26) or their reverse alphabetical position (A=26, B=25, ..., Z=1).

Let's consider the reverse alphabetical positions of the letters in TOGETHER:

• T: Its position from the end is 7 (Z=1, Y=2, ... T=7)
• O: Its position from the end is 12
• G: Its position from the end is 20
• E: Its position from the end is 22
• T: Its position from the end is 7
• H: Its position from the end is 19
• E: Its position from the end is 22
• R: Its position from the end is 9

Now, let's sum these reverse alphabetical positions:

\(\text{Sum for TOGETHER} = 7 + 12 + 20 + 22 + 7 + 19 + 22 + 9 = 118\)

The coded value for TOGETHER is 119. We can observe that \(118 + 1 = 119\).

Let's test this potential rule (sum of reverse alphabetical positions + 1) with the second word, MASTER.

Reverse alphabetical positions of the letters in MASTER:

• M: Its position from the end is 14
• A: Its position from the end is 26
• S: Its position from the end is 8
• T: Its position from the end is 7
• E: Its position from the end is 22
• R: Its position from the end is 9

Sum of these reverse alphabetical positions:

\(\text{Sum for MASTER} = 14 + 26 + 8 + 7 + 22 + 9 = 86\)

The coded value for MASTER is 87. We can see that \(86 + 1 = 87\).

The pattern is consistent: The code for a word is the sum of the reverse alphabetical positions of its letters plus 1.

Applying the Pattern to REVERSE

Now, let's apply the identified rule to the word REVERSE to find its code.

First, find the reverse alphabetical position for each letter in REVERSE:

• R: Its position from the end is 9
• E: Its position from the end is 22
• V: Its position from the end is 5
• E: Its position from the end is 22
• R: Its position from the end is 9
• S: Its position from the end is 8
• E: Its position from the end is 22

Next, sum these reverse alphabetical positions:

\(\text{Sum for REVERSE} = 9 + 22 + 5 + 22 + 9 + 8 + 22\)

\(\text{Sum for REVERSE} = 97\)

Finally, apply the '+ 1' part of the rule:

\(\text{Code for REVERSE} = \text{Sum} + 1 = 97 + 1 = 98\)

So, the word REVERSE is coded as 98 in this language.

The final answer is 98.

Revision Table: Key Concepts

Additional Information: Reverse Alphabetical Positions

Understanding reverse alphabetical positions is crucial for solving many coding-decoding questions. The reverse position is simply how far a letter is from the end of the alphabet.

For example:

• A is the 1st letter, its reverse position is 26 (27-1).
• B is the 2nd letter, its reverse position is 25 (27-2).
• Z is the 26th letter, its reverse position is 1 (27-26).

Here is a list of letters and their reverse alphabetical positions:

Memorizing or quickly calculating these positions can help solve such coding questions more efficiently during exams.