In a code language, 'FAMOUS' is coded as 'UZNLFH' and 'SLOW' is coded as 'HOLD'. How will 'RUMOUR' be coded in the same language?

Let's check the relation between the letters of the word and their code by looking at pairs of opposite letters (where sum of positions = 27):
First word: FAMOUS → UZNLFH
Let's look at the letters from last to first (reversed order):

Opposite of S is H

Opposite of U is F

Opposite of O is L

Opposite of M is N

Opposite of A is Z

Opposite of F is U
So, reversing the opposite letters of FAMOUS (which are U, Z, N, L, F, H) gives UZNLFH. Let's check direct correspondence instead:

F (6) ↔ U (21) → Opposites

A (1) ↔ Z (26) → Opposites

M (13) ↔ N (14) → Opposites

O (15) ↔ L (12) → Opposites

U (21) ↔ F (6) → Opposites

S (19) ↔ H (8) → Opposites
The letters are directly replaced by their respective opposite English alphabet letters!

Second word: SLOW → HOLD

S ↔ H

L ↔ O

O ↔ L

W ↔ D
This confirms the direct opposite letter logic.

Applying this to RUMOUR:

Opposite of R is I

Opposite of U is F

Opposite of M is N

Opposite of O is L

Opposite of U is F

Opposite of R is I

The resulting code is IFNLFI.