In a certain code, TEACHER is written as VGCEJGT. How will CHILDREN be written…

Concept

In a fixed letter-shift code, the same alphabetic displacement is applied to every letter. The rule is identified by comparing corresponding letters in the given pair and confirming that the displacement stays constant.

Application

1. Compare TEACHER with VGCEJGT: T becomes V, E becomes G, A becomes C, C becomes E, H becomes J, E becomes G, and R becomes T. Every letter moves two places forward in the alphabet.

2. Apply the same +2 shift to CHILDREN: C becomes E, H becomes J, I becomes K, L becomes N, D becomes F, R becomes T, E becomes G, and N becomes P.

Cross-check

Reverse each letter of EJKNFTGP by two alphabet positions. The sequence returns E to C, J to H, K to I, N to L, F to D, T to R, G to E, and P to N, which reconstructs CHILDREN.

Contrast

• EKNJFTGP places K, N, and J in the second, third, and fourth coded positions, so it does not preserve the uniform +2 mapping for H, I, and L.

• EJKNFTGP gives the +2 image of every letter in CHILDREN.

• KNJFGTP begins with K and N, which are not the +2 images of C and H.

• The transformed sequence is present among the listed code strings, so the residual choice is unnecessary.

Therefore, the code for CHILDREN is EJKNFTGP.