In a certain code language, ‘BOTH’ is written as ‘DQVJ’ and ‘DARE’ is written as ‘FCTG’ How will ‘WILL’ be written in that language?

Correct — B. Rule: every letter moves +2 places in the alphabet.

BOTH → DQVJ: B+2=D, O+2=Q, T+2=V, H+2=J.
DARE → FCTG: D+2=F, A+2=C, R+2=T, E+2=G.

Both samples agree, so apply the same step to WILL:
W+2=Y, I+2=K, L+2=N, L+2=N.

That gives YKNN → option (b).

Why the others are wrong

• (a)
  YJMN — YJMN moves the first and last letters by 2 but the middle two by 1. Under this code I becomes K, not J.
• (c)
  XJMM — XJMM is the whole word shifted +1. Both sample words fix the step at +2.
• (d)
  XKNM — XKNM mixes the steps — X is W+1 while K is I+2. A code of this kind uses one step for every letter.

Letter-shift codes are the simplest coding family: turn each letter into its position, add or subtract a fixed number, turn it back. The two given words exist to fix that number and to prove it holds at every position.

Check both samples before shifting anything. If the two disagree, the step is not constant — it may alternate, or depend on the letter's place in the word — and a blind +2 will fail.

Key facts

• BOTH becomes DQVJ and DARE becomes FCTG under a uniform +2 shift.
• WILL under a +2 shift is YKNN.
• A letter repeated in the plain word stays repeated under a constant shift.

Common traps

• Reading the step off one sample word only
• Counting the letter itself as the first step, so W lands on X instead of Y
• Ignoring the repeated L, which by itself removes two options

No directly related past PYQ was found.