Question

If ‘ORANGE' is coded as ‘PSBOHF', how is ‘GRAPES' coded?

• A. \(HSBQFT\)
• B. \(HRBQFT\)
• C. \(HSBQFS\)
• D. \(GSBQFT\)

Hint:

Convert two or three letter pairs from the given example into their alphabet positions and find the numeric difference between each pair. If that difference stays the same every time, it is the shift to apply to every letter of the new word.

Answer 1

The Correct Option is A

Concept: In coding–decoding problems, each letter of a word is replaced using a certain pattern or rule. Here, every letter in the word is shifted one step forward in the alphabetical order.

Step 1: Observe the pattern in the given example. \[ O \rightarrow P \] \[ R \rightarrow S \] \[ A \rightarrow B \] \[ N \rightarrow O \] \[ G \rightarrow H \] \[ E \rightarrow F \] Thus, each letter is increased by \(+1\).

Step 2: Apply the same rule to the word ‘GRAPES'. \[ G \rightarrow H \] \[ R \rightarrow S \] \[ A \rightarrow B \] \[ P \rightarrow Q \] \[ E \rightarrow F \] \[ S \rightarrow T \]

Step 3: Write the coded word. \[ GRAPES \rightarrow HSBQFT \] Thus, the required code is: \[ \boxed{HSBQFT} \]

Answer 2

Concept:

• A letter-shift code can be treated as ordinary arithmetic by numbering the letters $A=0, B=1, \dots, Z=25$, so the encoding rule becomes $\text{code}(x) = (x+s) \bmod 26$ for some fixed shift $s$.
• The shift $s$ can be found from the given example and should be confirmed with more than one letter pair before it is trusted.

Step 1: Convert one letter pair from the given example to numbers to find the shift.
$O$ is the 15th letter, so $O = 14$ (0-indexed). $P$ is the 16th letter, so $P = 15$.
Shift $s = 15 - 14 = 1$

Step 2: Confirm the same shift with another pair from the example.
$E = 4$, $F = 5$, so shift $= 5 - 4 = 1$, the same value. The rule $s = 1$ is confirmed, not a coincidence.

Step 3: Convert each letter of GRAPES to its 0-indexed number.
$G = 6,\ R = 17,\ A = 0,\ P = 15,\ E = 4,\ S = 18$

Step 4: Apply $\text{code}(x) = (x+1) \bmod 26$ to each value and convert back to letters.
$G: 6+1=7 \to H$
$R: 17+1=18 \to S$
$A: 0+1=1 \to B$
$P: 15+1=16 \to Q$
$E: 4+1=5 \to F$
$S: 18+1=19 \to T$

Final Answer: $HSBQFT$