In a certain code language, ‘EAGLE’ is written as ‘DZFKD’ and ‘DREAM’ is written as ‘CQDZL’. How will ‘SINCE’ be written in that language?

Correct — B. Line each code letter up under its plain letter and the same shift appears everywhere.

Rule: every letter moves back one place, with A wrapping round to Z.

EAGLE to DZFKD: E to D, A to Z, G to F, L to K, E to D
DREAM to CQDZL: D to C, R to Q, E to D, A to Z, M to L

Now take SINCE one letter at a time:
S to R, I to H, N to M, C to B, E to D

That spells RHMBD — option (b).

Why the others are wrong

• (a)
  THMDF — THMDF is not one rule at all. Its T, D and F each run one place forward while its H and M run one place back, so it mixes the two directions.
• (c)
  RJOBD — RJOBD gets R, B and D right but sends J and O forward — I to J and N to O — where the code sends every letter back.
• (d)
  TJODF — TJODF shifts every letter forward by one. It is the answer you reach by reading DZFKD as the plain word and EAGLE as its code, which reverses the direction of the whole cipher.

A shift cipher is settled by subtraction, not by inspection. Take the position of each code letter, subtract the position of its plain letter, and if the same number comes out every time you have the rule.

Both solved words matter. One word can be fitted by a rule that fails on the next, so the second word is the confirmation step, not a repetition.

The wrap is the part that costs marks: at −1, A does not stay A, it becomes Z.

Key facts

• EAGLE becomes DZFKD under a shift of −1, with A wrapping to Z.
• DREAM becomes CQDZL under the same −1 shift, which confirms the rule on a second word.
• S = 19, I = 9, N = 14, C = 3 and E = 5, so SINCE shifted back one gives R, H, M, B and D.

Common traps

• Running the shift forward instead of backward, which turns SINCE into TJODF.
• Mis-handling the wrap and leaving A as A instead of moving it to Z.

No directly related past PYQ was found.