Question

In a code language, \(m^{\text{th}}\) letter is coded as \((m-1)^{\text{th}}\) letter if \(m\) is odd and \((m+1)^{\text{th}}\) letter if \(m\) is even. Then the word that is coded as ‘FZHO’ is

• A. GAIL
• B. GAIN
• C. RAIN
• D. GARE

Hint:

In coding questions, convert letters into alphabet positions and apply the given rule carefully.

Answer 1

The Correct Option is B

Concept:
The coding rule is: \[ m\text{ odd}\Rightarrow m^{th}\text{ letter is coded as }(m-1)^{th}\text{ letter} \] \[ m\text{ even}\Rightarrow m^{th}\text{ letter is coded as }(m+1)^{th}\text{ letter} \] We need to find the original word which gives the code \[ \text{FZHO} \]

Step 1: Test option GAIN. Letters of GAIN are: \[ G,\ A,\ I,\ N \] Their positions are: \[ G=7,\quad A=1,\quad I=9,\quad N=14 \]

Step 2: Apply the coding rule. For \(G=7\), \(7\) is odd, so code is \(7-1=6\): \[ G\rightarrow F \] For \(A=1\), \(1\) is odd, so code is \(1-1\). In alphabet coding, moving one step back from \(A\) gives \(Z\): \[ A\rightarrow Z \] For \(I=9\), \(9\) is odd, so code is \(9-1=8\): \[ I\rightarrow H \] For \(N=14\), \(14\) is even, so code is \(14+1=15\): \[ N\rightarrow O \]

Step 3: Form the coded word. \[ \text{GAIN}\rightarrow \text{FZHO} \] This matches the given code.

Step 4: Final answer. \[ \boxed{\text{GAIN}} \]