In a certain code language, ‘TIDE’ is coded as ‘9457’ and ‘DENT’ is coded as ‘7593’. What is the code for ‘N’ in that language?

Correct — D.

Rule: the digits are jumbled, so match by what the two words share, not by position.

TIDE uses the letters T, I, D, E and the digits 9, 4, 5, 7.
DENT uses the letters D, E, N, T and the digits 7, 5, 9, 3.

Letters in both words: D, E, T. Digits in both codes: 9, 5, 7.
So D, E and T take 9, 5 and 7 between them, in some order.

That leaves exactly one unmatched letter and one unmatched digit in each word.
In TIDE the leftovers are I and 4, so I = 4.
In DENT the leftovers are N and 3.

N = 3 → option (d).

Why the others are wrong

• (a)
  5 — 5 appears in both codes. A digit printed in TIDE's code and in DENT's code must belong to one of the shared letters D, E or T, so it cannot stand for N, which occurs in DENT alone.
• (b)
  9 — 9 is shared as well. It sits in the D, E, T group. N appears in only one of the two words, so its digit has to appear in only one of the two codes.
• (c)
  7 — 7 is the third shared digit, tied like 9 and 5 to D, E or T; the digit unique to DENT's code is 3.

In this family of codes each letter has a fixed digit, but the digits are not printed in the order of the letters. Reading them position for position is what wrecks the question.

The method is set intersection. Letters common to both words must correspond to digits common to both codes, so put those aside as one block without deciding which is which.

What remains is a one-to-one leftover in each word, and the leftover pair solves itself. You never need to know that D is 7 or 5 to answer for N.

Key facts

• TIDE and DENT share the letters D, E and T, and their codes share the digits 9, 5 and 7.
• A letter unique to one word must map to a digit unique to that word's code.
• The codes are not position for position: reading them that way would make D equal 5 and 7 at once.

Common traps

• Reading the code position for position, which contradicts itself on the very first letter.
• Choosing a digit that appears in both codes for a letter that appears in only one word.
• Solving the shared letters first, which is unnecessary and slow.

No directly related past PYQ was found.