Understanding the Coding Pattern

The question asks us to find the code for the word FUND based on the given example where RATE is coded as IZGV. We need to identify the coding logic.

Let's examine the letter pairs between RATE and IZGV:

• R → I
• A → Z
• T → G
• E → V

We can determine the relationship by looking at the reverse positions in the alphabet (A=1, Z=26). The reverse of a letter at position $n$ is at position $26 - n + 1$.

• R is the 18th letter. Its reverse position is $26 - 18 + 1 = 9$, which corresponds to the letter I.
• A is the 1st letter. Its reverse position is $26 - 1 + 1 = 26$, which corresponds to the letter Z.
• T is the 20th letter. Its reverse position is $26 - 20 + 1 = 7$, which corresponds to the letter G.
• E is the 5th letter. Its reverse position is $26 - 5 + 1 = 22$, which corresponds to the letter V.

The coding logic is confirmed as the substitution of each letter with its reverse alphabet counterpart.

Applying the Pattern to FUND

We now apply this reverse alphabet substitution rule to the word FUND:

• F is the 6th letter. Its reverse position is $26 - 6 + 1 = 21$. The 21st letter is U.
• U is the 21st letter. Its reverse position is $26 - 21 + 1 = 6$. The 6th letter is F.
• N is the 14th letter. Its reverse position is $26 - 14 + 1 = 13$. The 13th letter is M.
• D is the 4th letter. Its reverse position is $26 - 4 + 1 = 23$. The 23rd letter is W.

Combining these results, the word FUND is coded as UFMW.