In certain code languages the word “PACK” is written in four different code languages. Understanding the code, find out the correct code language for the word given in each of the following questions.
(1) TEGO
(2) MXZH
(3) VFGO
(4) QDHR
RAIN = NXFK
CROP = DUTW
SAND = WERH

Hint: In this problem, we are given a word and some of the relevant code languages. We have to find how the given word is encoded or decoded into the following given options. We should know that in mathematics encoding or decoding is encrypt or decrypt a word in a particular code or pattern based on some set of rules. We can now understand the code and find out the correct code language for the given word.

Complete step by step answer:
Here we have to understand the code and find out the correct code language for the given word.
The given word is “PACK”
We can now take the first option, TEGO.
We can see that T comes after three letters from P, similarly E, G, O comes after three letters form A, C and K respectively.
We can now find the second option MXZH.
We can now see that M comes two words before P, similarly X, Z, H comes two letters before A, C and K respectively.
\[\begin{align}
  & P\underset{\leftarrow ON}{\mathop \to }\,M \\
 & A\underset{\leftarrow ZY}{\mathop \to }\,X \\
 & C\underset{\leftarrow BA}{\mathop \to }\,Z \\
 & K\underset{\leftarrow JI}{\mathop \to }\,H \\
\end{align}\]
We can now find the third option VFGO.
Here we can see that, V comes after 6 letters form P, F comes after four letters form A, G and O comes after 3 letters form C and K respectively.
\[\begin{align}
  & P\underset{QRSTUV}{\mathop \to \text{ }}\,V \\
 & A\underset{BCDE}{\mathop \to }\,F \\
 & C\underset{DEF}{\mathop \to }\,G \\
 & K\underset{LMN}{\mathop \to }\,O \\
\end{align}\]
We can now find the fourth option QDHR.
We can see that Q comes after P, D comes 2 letters after A, H comes four letters after C and R comes 6 letters after K.
\[\begin{align}
  & P\to Q \\
 & A\underset{BC}{\mathop \to }\,D \\
 & C\underset{DEFG}{\mathop \to }\,H \\
 & K\underset{LMNOPQ}{\mathop \to }\,R \\
\end{align}\]
We can now find for,
RAIN = NXFK
\[\begin{align}
  & R\underset{\leftarrow QPO}{\mathop \to }\,N \\
 & A\underset{\leftarrow ZY}{\mathop \to }\,X \\
 & I\underset{\leftarrow HG}{\mathop \to }\,F \\
 & N\underset{\leftarrow ML}{\mathop \to }\,K \\
\end{align}\] \[\]
CROP = DUTW
\[\begin{align}
  & \text{C}\to \text{D} \\
 & R\underset{ST}{\mathop \to }\,U \\
 & O\underset{PQRS}{\mathop \to }\,T \\
 & P\underset{QRSTUV}{\mathop \to }\,W \\
\end{align}\]
SAND = WERH
\[\begin{align}
  & S\underset{TUV}{\mathop \to }\,W \\
 & A\underset{BCD}{\mathop \to }\,E \\
 & N\underset{OPQ}{\mathop \to }\,R \\
 & D\underset{EFG}{\mathop \to }\,H \\
\end{align}\].
Similarly, we can code for every word given.

Note: We should always remember the concept of coding and decoding as that in mathematics encoding or decoding is encrypt or decrypt a word in a particular code or pattern based on some set of rules. We can now understand the code and find out the correct code language for the given word.