In a certain code language, 'BOOK' is coded as 'DMRH' and 'WELL' is coded as 'YCOI'. How will 'TREE' be coded in the same language?
To solve the problem of decoding the word 'TREE' using the code language pattern provided, let's first identify the pattern used to code the words 'BOOK' and 'WELL'.
Step-by-step Explanation:
- The word 'BOOK' is coded as 'DMRH'. Let's examine the transformation:
| Letter | B | O | O | K |
|---|---|---|---|---|
| Coded Letter | D | M | R | H |
| Alphabet Position | 2 | 15 | 15 | 11 |
| Coded Position | 4 | 13 | 18 | 8 |
- The shift in letters is calculated as follows:
- \(B \to D\): Shift of \(2\) positions forward.
- \(O \to M\): Shift of \(-2\) positions backward.
- \(O \to R\): Shift of \(3\) positions forward.
- \(K \to H\): Shift of \(-3\) positions backward.
- Now, let's analyze the coding for 'WELL' to confirm the pattern:
| Letter | W | E | L | L |
|---|---|---|---|---|
| Coded Letter | Y | C | O | I |
| Alphabet Position | 23 | 5 | 12 | 12 |
| Coded Position | 25 | 3 | 15 | 9 |
- The shift in letters is the same as the previous coding:
- \(W \to Y\): Shift of \(2\) positions forward.
- \(E \to C\): Shift of \(-2\) positions backward.
- \(L \to O\): Shift of \(3\) positions forward.
- \(L \to I\): Shift of \(-3\) positions backward.
- Using the identified pattern (positions +2, -2, +3, -3), apply this to the word 'TREE':
| Letter | T | R | E | E |
|---|---|---|---|---|
| Alphabet Position | 20 | 18 | 5 | 5 |
| Coded Position | 22 | 16 | 8 | 2 |
| Coded Letter | V | P | H | B |
The coded word for 'TREE' is 'VPHB'. Therefore, the correct answer is VPHB.
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