In a certain code language, 'CASE' is written as 'FTBD' and 'CAKE' is written as 'FLBD'. How will 'CALF' be written in that language?

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Let's analyze the given code:

1. CASE -> FTBD
2. CAKE -> FLBD

Check letter-wise transformation:

- C -> F (C is 3rd letter, F is 6th letter; +3)
- A -> T or L? Let's check carefully.

From CASE to FTBD:
C(3) -> F(6) (+3)
A(1) -> T(20) (+19)
S(19) -> B(2) (Since 19 to 2 is -17 or +9 if we consider modulo 26)
E(5) -> D(4) (-1)

From CAKE to FLBD:
C(3) -> F(6) (+3)
A(1) -> L(12) (+11)
K(11) -> B(2) (-9 or +17)
E(5) -> D(4) (-1)

The transformations for A and the third letter differ between the two words, so let's check the pattern by position:

Position 1 (C): +3 (C->F)
Position 4 (E): -1 (E->D)

Positions 2 and 3 vary:
- For CASE: A->T (+19), S->B (-17)
- For CAKE: A->L (+11), K->B (-9)

Notice that the 3rd letter in both cases is converted to B.

Now, let's check the difference between S and K:
S(19), K(11), difference is 8.

The 2nd letter A is converted differently: T(20) and L(12), difference 8.

So, the 2nd and 3rd letters are shifted by +19 and -17 in CASE, and +11 and -9 in CAKE, both pairs differ by 8.

This suggests the code depends on the 3rd letter:
- For S (19), shifts are +19 and -17
- For K (11), shifts are +11 and -9

Now, let's apply the same logic to CALF:

Letters: C(3), A(1), L(12), F(6)

Position 1: C -> F (+3)
Position 4: F -> E (F(6) -1 = E(5)) but in previous examples E->D (-1), so F->E (-1)

Position 2 and 3 shifts depend on the 3rd letter L(12):
- For K(11), shifts were +11 and -9
- For L(12), shifts should be +12 and -10 (incremented by 1)

So:
Position 2: A(1) +12 = 13 -> M
Position 3: L(12) -10 = 2 -> B

So the coded word is:
Position 1: F
Position 2: M
Position 3: B
Position 4: E

But none of the options match FMBe.

Check if the last letter shift is always -1:
In given examples, E->D (-1)
So F(6) -1 = E(5)

But options have D at the end, so maybe last letter is always D.

Try last letter as D:

So final code: F M B D

But options start with G, not F.

Check if position 1 shift is +4 instead of +3:
C(3) +4 = 7 -> G

Try this:
Position 1: C(3) +4 = G(7)
Position 2: A(1) +12 = M(13)
Position 3: L(12) -10 = B(2)
Position 4: F(6) -1 = E(5)

GM B E
No E at end in options, but D is close.

Try last letter shift -2:
F(6) -2 = D(4)

So code: G M B D

Option 1: GMDB
Option 3: GMBD

Check order of last two letters:
In CASE and CAKE, last two letters are BD.
So last two letters are B and D.

So code is G M B D

Hence, the correct code is GMBD.

Check options:
Option 3: GMBD

Therefore, the answer is option 3: GMBD.

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